Topic 5 All questions-numbered

5 Electricity and magnetism 5.1 Electric fields Name: ………………………………. Date: ………………………………. Electric fields 1 Assume conventional directions; i.e. left is west. 1 Identical point charges of 9.3 nC are 0.47 mm apart. Calculate the force between the two charges. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 2 Calculate the total force on charge A. All three charges are 2.5 ȝC. The distance from A to B is 2.0 m and from B to C is 2.0 m and angle B is 90o. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 Calculate the electric field 0.245 cm from a point charge of 25.6 nC. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 1 1 5.1 Electric fields 4 Charge A is 27 nC and B is 81 nC. Where will the electric field be equal to zero? See below for the diagram. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 5 What is the electric field 2.0 mm from charge B and 4.0 mm from A in the above question? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 6 Determine the electric field at point P if charge A = 25.0 ȝC and B = –50.0 ȝC and distance AP is 5.00 cm and BP is 12.0 cm. Assume that angle P is 90o. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 2 2 5 Electricity and magnetism 5.1 Electric fields Name: ………………………………. Date: ………………………………. Electric fields 2 1 How much charge passes through a wire in 2.5 minutes if the current in the wire is 1.6 A? .................................................................................................................................................................................. .................................................................................................................................................................................. 2 842 C of charge passes through a circuit in 3.25 minutes. What is the current in the circuit? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 The cross-sectional area of a wire containing 0.67 A is 4.9 × 10–7 m2. If there are 8.5 × 1028 charge carriers per m3 in this wire, what is the drift speed of the charge carriers? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 4 The energy transfer to a device is 112 000 J when there is a potential difference of 185 volts across it. If the current through the device is 0.0644 A, how long in hours is the current flowing? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 5 312 C of charge passes through an electrical device in 143 seconds. If the potential difference across the device is 2.88 volts, determine the energy transfer to the device. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 6 A cell produces a steady current of 0.0044 A during its lifetime of 96 hours. Determine the maximum energy that this 1.5 V (terminal voltage) cell provides. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 1 5.1 Electric fields 7 The power dissipated in a 6.0 V device is 3.0 watts. What current is flowing through the device? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 8 In 5.5 hours how much energy is transferred to the device in question 7? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 9 An electron is accelerated to a speed of 4.23 × 106 ms–1 from rest by a potential difference. Calculate the potential difference. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 4 2 5 Electricity and magnetism 5.2 Heating effect of electric current Name: ………………………………. Date: ………………………………. Worksheet 1 1 The potential difference across a component is 24 volts when the current through it is 0.40 amps. What is the resistance of the component? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 2 6.00 metres of a wire yields a resistance of 84.0 ȍ. If the resistivity of the wire is 4.30 × 10–7 ȍm, find the diameter of the wire. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 The resistance of a certain length of wire is 12 ȍ. If the wire is replaced with another wire of the same substance but half the length and twice the diameter, what will be the new resistance? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 4 Find the total resistance of the arrangement below. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 5 1 5 Electricity and magnetism 5.2 Heating effect of electric current Name: ………………………………. Date: ………………………………. Worksheet 2 1 Find the total resistance of the arrangement below. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 2 Calculate the potential difference across each resistor and the current through the resistors. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 If the value of each resistor is doubled in question 2, what will be the potential difference across each resistor and the current through the resistors? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 6 1 5.2 Heating effect of electric current 4 A 12 volt supply is in series with a resistor and an LDR. In light, the LDR has a potential difference of 3.0 volts and in the dark it has a potential difference of 6.0 volts. Find the ratio of the series resistor to the resistance of the LDR in light. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 5 A 12 ȍ resistor has a potential difference of 4.0 volts. Determine the power dissipated in the resistor. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 6 The power dissipated in a resistor is 240 watts when a voltage of 220 volts is across it. If the voltage is cut in half, what is the power dissipation in the resistor? .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 7 2 5 Electricity and magnetism 5.2 Heating effect of electric currents Name: ………………………………. Date: ………………………………. Worksheet 3 1 Calculate the currents below. 2 Determine V2 if the resistance of the voltmeter is 10.0 kȍ. ................................................................................................................................................................................... ................................................................................................................................................................................... ................................................................................................................................................................................... ................................................................................................................................................................................... 3 Repeat question 2 replacing the 10.0 kȍ voltmeter with a 100.0 kȍ voltmeter. ................................................................................................................................................................................... ................................................................................................................................................................................... ................................................................................................................................................................................... ................................................................................................................................................................................... 8 1 5 Electricity and magnetism 5.3 Electric cells Name: ………………………………. Date: ………………………………. Worksheet 1 1 The following graph is a result of an internal resistance experiment. a What is the emf of the battery? ........................................................................................................................................................................... ........................................................................................................................................................................... b What is the internal resistance of the cell? ........................................................................................................................................................................... ........................................................................................................................................................................... c What is the value of the load resistor when the current equals 1.98 A? ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... d Define emf, terminal voltage, and internal resistance. ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... e At what value of load resistance will the power delivered to the load be at a maximum? ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... ........................................................................................................................................................................... f Draw and label the circuit used in this experiment. 9 1 5 Electricity and magnetism 5.3 Electric cells Name: ………………………………. Date: ………………………………. Worksheet 2 1 A cell supplies a current of 4.20 mA for 925 hours. What is its rating? .................................................................................................................................................................................. .................................................................................................................................................................................. 2 0.800 watts of power are dissipated in a cell of emf 10.0 volts. If the internal resistance is 2.40 ȍ, find the resistance of the load and the current in the load. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 3 A cell of emf 8.0 V has an internal resistance of 1.7 ȍ and is connected to a 4.9 ȍ resistor. Find the current in the resistor, the power dissipated in the resistor, and the terminal potential difference across the cell. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 4 A battery is connected in series with a variable resistor. When the resistor is 8.50 ȍ, the current is 1.00 A and when the resistor is 6.50 ȍ, the current is 1.25 A. What is the value of the internal resistance? .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 5 A cell supplies 5600 J of energy when 4200 C of charge moves completely around the circuit. The load resistor is 7.5 ȍ and the potential difference across the load is 1.1 V. Find the emf, the current through the circuit, and the size of the internal resistance of the cell. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. .................................................................................................................................................................................. 10 1 5.3 Electric cells 6 The following current and terminal voltage of a cell were recorded during an experiment. Determine the emf and the internal resistance of the cell. Current Terminal voltage 4.00 2.00 3.33 3.33 2.86 4.29 2.50 5.00 2.22 5.56 2.00 6.00 1.82 6.36 1.67 6.67 1.54 6.92 1.43 7.14 .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. .............................................................................................................................................................................. 11 2 5 E LE CTRIC IT Y AN D MAGN E TISM Questions 1 The electric force between them is + F (i.e. attractive). The spheres are touched together and are then returned to their original separation. (IB) Four point charges of equal magnitude, are held at the corners of a square as shown below. 2a +Q +Q a) Calculate the charge on X and the charge on Y. b) Calculate the value of the electric force between them after being returned to their original separation. (7 marks) 2a P 4 −Q −Q (IB) Two charged plastic spheres are separated by a distance d in a vertical insulating tube, as shown. tube spheres The length of each side of the square is 2a and the sign of the charges is as shown. The point P is at the centre of the square. d a) (i) Determine the magnitude of the electric field strength at point P due to one of the point charges. (ii) On a copy of the diagram above, draw an arrow to represent the direction of the resultant electric field at point P. The charge on each sphere is doubled. Friction with the walls of the tube is negligible. (iii) Determine, in terms of Q, a and k, the magnitude of the electric field strength at point P. (7 marks) 2 (IB) Two point charges of magnitude +2Q and −Q are fixed at the positions shown below. Discuss the direction of the electric field due to the two charges between A and B. Suggest at which point the electric field is most likely to be zero. (3 marks) −Q A 3 + + +2Q conductor X (5 marks) 5 (IB) a) Electric fields may be represented by lines of force. The diagram below shows some lines of force. B (IB) Two identical spherical conductors X and Y are mounted on insulated stands. X carries a charge of +6.0 nC and Y carries a charge of –2.0 nC. +6.0 nC Deduce the new separation of the spheres. A B −2.0 nC insulated stands conductor Y 240 12 (i) State whether the field strength at A and at B is constant, increasing or decreasing, when measured in the direction from A towards B. QUESTIONS d) An alternative circuit for measuring the V–I characteristic uses a potential divider. (ii) Explain why field lines can never touch or cross. b) The diagram below shows two insulated metal spheres. Each sphere has the same positive charge. (i) Draw a circuit that uses a potential divider to enable the V–I characteristics of the filament to be found. (ii) Explain why this circuit enables the potential difference across the lamp to be reduced to 0 V. (13 marks) + + 7 (IB) The graph below shows the V–I characteristic for two 12 V filament lamps A and B. lamp B 12 6 potential difference/V Copy the diagram and in the shaded area between the spheres, draw the electric field pattern due to the two spheres. (8 marks) lamp A (IB) A lamp is at normal brightness when there is a potential difference of 12 V across its filament and a current in the filament of 0.50 A. 0 a) For the lamp at normal brightness, calculate: 0 0.5 current/A 1.0 a) (i) Explain why the graphs indicate that these lamps do not obey Ohm’s law. (i) the power dissipated in the filament (ii) the resistance of the filament. (ii) State and explain which lamp has the greater power dissipation for a potential difference of 12 V. b) In order to measure the voltage–current (V–I) characteristics of the lamp, a student sets up the following electrical circuit. The two lamps are now connected in series with a 12 V battery as shown below. 12 V battery 12 V battery State the correct positions of an ideal ammeter and an ideal voltmeter for the characteristics of the lamp to be measured. lamp A lamp B b) (i) State how the current in lamp A compares with that in lamp B. c) The voltmeter and the ammeter are connected correctly in the previous circuit. Explain why the potential difference across the lamp (ii) Use the V–I characteristics of the lamps to deduce the total current from the battery. (i) cannot be increased to 12 V (iii) Compare the power dissipated by the two lamps. (11 marks) (ii) cannot be reduced to zero. 241 13 5 E LE CTRIC IT Y AN D MAGN E TISM 8 (IB) R X a) Explain how the resistance of the filament in a filament lamp can be determined from the V–I characteristic of the lamp. 2.0 Ω b) A filament lamp operates at maximum brightness when connected to a 6.0 V supply. At maximum brightness, the current in the filament is 120 mA. E (i) Copy the graph in (a), and draw the I–V characteristics for the resistor R. (i) Calculate the resistance of the filament when it is operating at maximum brightness. (ii) You have available a 24 V supply and a collection of resistors of a suitable power rating and with different values of resistance. Calculate the resistance of the resistor that is required to be connected in series with the supply such that the voltage across the filament lamp will be 6.0 V. (4 marks) 9 (IB) The graph below shows the I–V characteristics for component X. I/A6 -4 -2 0 Battery Voltmeter 2 -6 10 (IB) A student is to measure the current–voltage (I–V) characteristics of a filament lamp. The following equipment and information are available. Filament lamp 4 -8 (ii) Determine the total potential difference E that must be applied across component X and across resistor R such that the current through X and R is 3.0 A. (7 marks) Ammeter 0 2 4 6 8 V/V -2 Potentiometer Information emf = 3.0 V, negligible internal resistance marked “3 V, 0.2 A” resistance = 30 kΩ, reads values between 0.0 and 3.0 V resistance = 0.1 Ω, reads values between 0.0 and 0.5 A resistance = 100 Ω a) For the filament lamp operating at normal brightness, calculate: -4 (i) its resistance -6 (ii) its power dissipation. The student sets up the following incorrect circuit. The component X is now connected across the terminals of a battery of emf 6.0 V and negligible internal resistance. V a) Use the graph to determine: (i) the current in component X (ii) the resistance of component X. b) A resistor R of constant resistance 2.0 Ω is now connected in series with component X as shown below. A b) (i) Explain why the lamp will not light. (ii) State the approximate reading on the voltmeter. Explain your answer. (6 marks) 242 14 QUESTIONS a) (i) State the value of the current for which the resistance of X is the same as the resistance of Y and determine the value of this resistance. 11 (IB) A particular filament lamp is rated at 12 V, 6.0 mA. It just lights when the potential difference across the filament is 6.0 V. A student sets up an electric circuit to measure the I–V characteristics of the filament lamp. (ii) Describe and suggest an explanation for the I–V characteristic of conductor Y. A b) The two conductors X and Y are connected in series with a cell of negligible internal resistance. The current in the conductors is 0.20 A. 100 kΩ 12 V S V Use the graph to determine: (i) the resistance of Y for this value of current (ii) the emf of the cell. In the circuit, shown below, the student has connected the voltmeter and the ammeter into the circuit incorrectly. (8 marks) 13 (IB) A cell of electromotive force (emf) E and internal resistance r is connected in series with a resistor R, as shown below. The battery has emf 12 V and negligible internal resistance. The ammeter has negligible resistance and the resistance of the voltmeter is 100 kΩ. r E The maximum resistance of the variable resistor is 15 Ω. R a) Explain, without doing any calculations, whether there is a position of the slider S at which the lamp will be lit. The cell supplies 8.1 × 103 J of energy when 5.8 × 103 C of charge moves completely round the circuit. The current in the circuit is constant. b) Estimate the maximum reading of the ammeter. (5 marks) a) Calculate the emf E of the cell. b) The resistor R has resistance 6.0 Ω. The potential difference between its terminals is 1.2 V. Determine the internal resistance r of the cell. 12 (IB) The graph below shows the current–voltage (I–V) characteristics of two different conductors X and Y. c) Calculate the total energy transfer in R. 0.50 0.45 d) Describe, in terms of a simple model of 0.40 electrical conduction, the mechanism by 0.35 which the energy transfer in R 0.30 takes place. (12 marks) Y X I/A 0.25 0.20 0.15 14 (IB) A battery is connected in series with a 0.10 resistor R. The battery transfers 2000 C of 0.05 charge completely round the circuit. During 0.00 this process, 2500 J of energy is dissipated 0.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 R and 1500 J is expended in the battery. V/V Calculate the emf of the battery. (3 marks) 243 15 5 E LE CTRIC IT Y AN D MAGN E TISM 15 (IB) A student connects a cell in series with a variable resistor and measures the terminal pd V of the cell for a series of currents I in the circuit. The data are shown in the table. V/V 1.50 1.10 0.85 0.75 0.60 0.50 The electric field strength is 3.8 × 105 V m–1 and the magnetic field strength is 2.5 × 10–2 T. Calculate the speed of the electron if the net force acting on it due to the fields is zero. (3 marks) I/mA 120 280 380 420 480 520 18 (IB) A straight wire lies in a uniform magnetic field as shown. current I magnetic field Use the data to determine the emf and internal resistance of the cell. (5 marks) θ 16 (IB) A battery is connected to a resistor as shown. The current in the wire is I and the wire is at an angle of θ to the magnetic field. The force per unit length on the conductor is F. Determine the magnetic field strength. (2 marks) 6.0 V 10 Ω V 19 (IB) A straight wire of length 0.75 m carries a current of 35 A. The wire is at right angles to a magnetic field of strength 0.058 T. Calculate the force on the wire. (2 marks) When the switch is open the voltmeter reads 12 V, when the switch is closed it reads 11.6 V. 20 (IB) An ion with a charge of +3.2 × 10–19 C and a mass of 2.7 × 10–26 kg is moving due south at a speed of 4.8 × 103 m s–1. It enters a uniform magnetic field of strength 4.6 × 10–4 T directed downwards towards the ground. Determine the force acting on the ion. (4 marks) a) Explain why the readings differ. b) (i) State the emf of the battery. (ii) Calculate the internal resistance of the battery. c) Calculate the power dissipated in the battery. (6 marks) 17 (IB) An electron enters a pair of electric and magnetic fields in a vacuum as shown in the diagram. region of magnetic field electron E + B 244 16 Topic 5.1a Electric Force and Field Problems Conceptual Questions (These questions are not in an IB style but instead designed to check your understanding of the concept of this topic. You should try your best to appropriately communicate your answer using prose) 1. The form of Coulomb’s law is very similar to that of Newton’s law of universal gravitation. What are the differences between these two laws? Compare also the gravitational mass and electric charge. 2. Explain why the test charges we use when measuring electric fields must be small. 3. If a negatively charged particle enters a region of uniform magnetic field which is perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer. (Neglect gravity and assume there is no electric field). 4. Can you set a resting electron into motion with a magnetic field? With an electric field? Explain. 17 Calculation Based 5. What is the magnitude of the electric force of attraction between an iron nucleus (q = +26e) and its inner most electron if the distance between them is 1.5x10-12m? [2 marks] 6. Particles of charge +75, +48 and -85μC are placed in a line as shown. The centre of one is 0.35m from each of the others. Calculate the resultant force of the +75 and -85μC charges on the central +48μC charge. [3 marks] 7. Three positive particles of equal charge, +11μC are located at the corners of an equilateral triangle of side 15.0cm. Calculate the magnitude and direction of the resultant force of the bottom particles on the top one. [4 marks] 18 8. What are the magnitude and direction of the electric field 20.0cm directly above an isolated 33.0x10-6C charge? 9. What is the magnitude of the acceleration experienced by an electron in an electric field of 750N/C? How does the direction of the acceleration depend on the direction of the field at that point? 10. How strong is the electric field between two parallel plates 5.8mm apart if the potential difference between them is 220V? 19 11. The electric field between two parallel plates connected to a 45V battery is 150V/m. How far apart are the plates? 12. Two parallel plates, connected to a 200-V power supply, are separated by an air gap. How small can the gap be if the air is not to become conducting by exceeding its breakdown value of E = 3x106V/m? 20 5.1b Electric Potential Difference Problems Conceptual Questions (These questions are not in an IB style but instead designed to check your understanding of the concept of this topic. You should try your best to appropriately communicate your answer using prose) 1. If two points are at the same potential, does this mean that no work is done in moving a test charge from one point to another? Does this imply that no force need be exerted? Explain. 2. If a negative charge is initially at rest in an electric field, will it move toward a region of higher potential or lower potential? What about a positive charge? How does the potential energy of the charge change in each instance? 3. Distinguish between (a) electric potential and electric field; (b) electric potential and electric potential energy. 4. An electron is accelerated by a potential difference of V. How much greater would its final speed be if it is accelerated with 4V? 21 Calculation-based Questions 1. How much work does the electric field do in moving a -7.7µC charge from ground to a point whose potential is +55V higher? 2. How much work does the electric field do in moving a proton from a point with a potential of +125V to a point where it is -55V Express your answer in joules and electron volts. 3. How much kinetic energy will an electron gain (in joules an eV) if it accelerates through a potential difference of 23,000V in a TV picture tube? 22 4. An electron acquires 7.45x10-16J of kinetic energy hen it is accelerated by an electric field from plate A to plate B. What is the potential difference between the plates, and which plate is at the higher potential? 5. What is the speed of (a) an electron, and (b) a proton with a kinetic energy of 3.2keV? 6. What potential difference is needed to give a helium nucleus (Q = 2e) 65.0keV of kinetic energy? 23 5.2a Current and Resistance Problems Conceptual Questions (These questions are not in an IB style but instead designed to check your understanding of the concept of this topic. You should try your best to appropriately communicate your answer using prose) 1. A mobile phone battery is labeled in mAh. What does this quantity measure about it? 2. When an electric cell is connected to a circuit, electrons flow away from the negative terminal in the circuit. But within the cell they flow to the negative terminal. Explain. 3. The equation P = V2/R indicates that the power dissipated in a resistor decreases if the resistance is increased, whereas the equation P = I2R implies the opposite. Is there a contradiction here? Explain. 4. Which draws the more current, a 100W lightbulb or a 75W lightbulb? Which has the higher resistance? 5. Is the current used up in a resistor? Explain. 24 Calculation-based Questions 1. A current of 1.30A flows in a wire. How many electrons are flowing past any point in the wire per second? 2. A service station charges a battery using a current of 6.7A for 5.0h. How much charge passes through the battery? 3. What is the current in amperes if 1200Na+ ions flow across a cell membrane in 3.5µs? The charge on the sodium is the same as on an electron, but positive. 4. What is the resistance of a toaster if 120V produces a current of 4.2A? 5. What voltage will produce 0.25A of current through a 3800Ω resistor? 6. A hair dryer draws 7.5A when plugged into a 120V line. (a) What is its resistance? (b) How much charge passes through it in 15min? 25 7. An electric clothes dryer has a heating element with a resistance of 9.6Ω. (a) What is the current in the element when it is connected to 240V? (b) How much charge passes through the element in 50min? 8. A 9.0V battery is connected to a bulb whose resistance is 1.6Ω. How many electrons leave the battery per minute? 9. A bird stands on an electric transmission line carrying 2800A. The line has 2.5x10-5Ω resistance per meter, and the bird’s feet are 4.0cm apart. What is the potential difference between the bird’s feet? 10. An electric device draws 6.50A at 240V. (a) If the voltage drops by 15%, what will be the current, assuming nothing else changes? (b) If the resistance of the device were reduced by 15%, what current would be drawn at 240V? 26 11. A 12V battery causes a current of 0.60A through a resistor. (a) What is its resistance, and (b) how many joules of energy does the battery lose in a minute? For questions 12 -16, use 5.6x10-8Ωm as the resistivity of tungsten, 1.68x10-8Ωm as the resistivity of copper and 2.65x10-8Ωm as the resistivity of aluminium. 12. What is the diameter of a 1.00m length of tungsten wire whose resistance is 0.32Ω? 13. What is the resistance of a 3.5m length of copper wire 1.5mm in diameter? 14. Calculate the ratio of the resistance of a 10.0m of aluminium wire 2.0mm in diameter, to 20.00m of copper wire 2.5mm in diameter. 27 15. Can a 2.5mm diameter copper wire have the same resistance as a tungsten wire of the same length? Give numerical details? 16. A certain copper wire has a resistance of 10.0Ω. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece? 28 5.2b Combination of resistors and Kirchoffs Laws Conceptual Questions (These questions are not in an IB style but instead designed to check your understanding of the concept of this topic. You should try your best to appropriately communicate your answer using prose) 1. For what use are batteries connected in series? For what use are they connected in parallel? Does it matter if the batteries are nearly identical or not in either case? (Question 11) 2. If two identical resistors are connected in series to a battery, does the battery have to supply more power of less power than when only one of the resistors is connected? Explain. (Question 7) 3. When applying Kirchoff’s loop rule, does the sign (or direction) of the batteries EMF depend on the direction of the current through the battery? What about the terminal voltage? (Question 9) 4. What happens to the voltage across each resistor when the switch S is closed? What happens to the power output of the battery when the switch is closed? (Problem 19) 29 Calculation-based Questions 1. A 650-Ω and 2200- Ω resistor are connected in series with a 12-V battery. What is the voltage across the 2200- resistor? 2. Suppose that you have a 680- a 940-Ω and a 1.20-kΩ resistor. What is (a) the maximum and (b) the minimum resistance you can obtain by combining these? 3. Determine (a) the equivalent resistance of the circuit and (b) the voltage across each resistor. 30 4. Let all the resistors shown to be equal to 125Ω and V = 22.0V. Determine the current through each resistor before and after closing the switch S. Compare your answer to question 4 above. 5. (HARD) Calculate the equivalent resistance of the following circuit. Assume all the resistors are equal to 2.8kΩ. 31 6. Use Kirchoff’s laws to calculate the current in the circuit and show that the sum of all the voltages around the circuit is zero. 7. (HARD) What is the potential difference between points a and d for the circuit below? 400Ω 32 8. Determine the magnitudes and directions of the currents through R1 and R2. 9. Calculate the currents in each resistor. 33 5.2c Potential Dividers Problems Calculation-based Questions 1. A potential divider circuit is shown below. The battery has negligible internal resistance and the voltmeter has a very high resistance. 1200Ω 6.0V X 400Ω Y a. Show that the voltmeter reading is 1.5V b. An electric device rated at 1.5V, 0.1A is connected between terminals X and Y. The device has constant resistance. The voltmeter reading drops to a very low value and the device fails to operate, even through the device itself is not faulty. i. Calculate the total resistance of the device and the 400Ω resistor in parallel. ii. Calculate the p.d. across the device when it is connected between X and Y. iii. Why does the device fail to operate? 34 2. The diagram below is a simple design for a ‘movement’ sensor used in an earthquake region. The supply has negligible resistance. 1.0Ω 5.0V 32cm To Computer Resistance wire A resistor wire is stretched between two rigid steel plates, not shown in the diagram. During an earthquake, ground movement changes the separation between the plates and so the length of wire changes. The wire has a radius of 0.62mm and length 32cm. It is made of a material of resistivity 6.8x10-6Ωm. a. Show that the resistance of the wire is 1.8Ω. b. Calculate the potential difference between A and B. c. The length of the wire increases. State and explain the effect on the p.d. between A and B. 3. If the thermistor in the diagram has a resistance R1 of 400Ω at 20°C and 100Ω at 70°C, calculate Vout at (a) 20°C and (b) 70°C. +5V R1 Vin 100Ω Vout 0V 35 5.3 Internal Resistance Problems Calculation-based Questions 1. Calculate the terminal voltage for a battery with an internal resistance of 0.900Ω and an emf of 8.50V when the battery is connected in series with (a) an 81.0Ω resistor, and (b) an 810Ω resistor. 2. Four 1.5V cells are connected in series to a 12Ω lightbulb. If the resulting current is 0.45A, what is the internal resistance of each cell, assuming they are identical and neglecting the wires? 3. What is the internal resistance of a 12.0V car battery whose terminal voltage drops to 8.4V when the starter draws 75A? What is the resistance of the starter? 4. A 1.5V dry cell can be tested by connecting it to a low resistance ammeter. It should be able to supply at least 22A. What is the internal resistance of the cell in this case, assuming it is much greater than that of the ammeter? 36 Topic 5.4 Magnetic Force and Field Problems Conceptual Questions (These questions are not in an IB style but instead designed to check your understanding of the concept of this topic. You should try your best to appropriately communicate your answer using prose) 1. Can you set a resting electron into motion with a magnetic field? With an electric field? Explain. 2. Can an iron rod attract a magnet? Can a magnet attract an iron rod? What must you consider to answer these questions? Calculation Based 3. The force on a wire is a maximum of 6.50x10-2N when placed between the pole faces of a magnet. The current flows horizontally to the right and the magnetic field is vertical. The wire is seen to “jump” toward the observer when the current is turned on. a. What type of magnetic pole is the top pole face? [1 mark] b. If the pole faces have a diameter of 10.0cm estimate the current in the wire if the field is 0.16T. [2 marks] c. If the wire is tipped so that it makes an angle of 10.0° with the horizontal, what force will it now feel? (Hint: You should draw the diagram). [1 mark] 37 4. Determine the magnitude and direction of the force on an electron travelling 8.75x105m/s horizontally to the East in a vertically upward magnetic field of strength 0.75T. [3 marks] 5. A 5.0 MeV (kinetic energy) proton enters a 0.20T field in a plane perpendicular to the field. What is the radius of its path? [3 marks] 6. (a) What is the magnitude of the force per meter of length on a straight wire carrying an 8.40A current when perpendicular to a 0.90T uniform magnetic field? (b) What if the angle between the wire and field is 45.0°? 7. Determine the magnitude and direction of the force on an electron travelling 8.75x105m/s horizontally to the east in a vertically upward magnetic field of strength 0.75T. 38 8. Alpha particles of charge q = +2e and mass m = 6.6x10-27kg are emitted from a radioactive source at a speed of 1.6x107m/s. What magnetic field strength would be required to bend them into a circular path of radius 0.25m? 9. A doubly charged helium atom whose mass is 6.6x10-27kg is accelerated by a voltage of 2100V. (a) What will be its radius of curvature if it moves in a plane perpendicular to a uniform 0.340T field? (b) What is its period of revolution? 39 Topic 5.1 – Electric fields Summative Assessment v1 NAME: _____________________________________ PERIOD: __ LEVEL: ____ THIS ASSESSMENT COUNTS AS EVIDENCE! Show formulas, substitutions, answers (in spaces) and units! A balloon becomes charged to 225 mC by rubbing it on Albert the Physics Cat. 1. What is the sign of the charge the balloon acquires? 1. _________________ 2. How many electrons are transferred between the balloon and Albert? 2. _________________ 3. How do the charges of the balloon and Albert compare? 3. _________________ The following questions are about electric current. 4. A +225 µC charge is moved past a point in a conductor in 15.0 ms. What is the value of the electric current involved in this movement? 4. _________________ 5. An electrical discharge between a cloud and a lightning rod has a current of 2150 A for a time of 2.15 ms. How much electric charge was involved in this lightning strike? 5. _________________ Two equal point charges of +225 µC are placed 0.125 mm apart. 6. If the charges are located in air, or vacuum, what is their electric force? Is it attractive or repulsive? 6. _________________ 7. If the charges now have a 0.125 mm layer of mica between them, what is the new electric force between them? Assume this purity of mica has a permittivity of 8.50 times that of free space. 7. _________________ A conducting sphere of radius 0.25 m holds an electric charge of Q = +40.0 µC. A charge q = +10.0 µC is located in the vicinity of Q. 8. Find the electric force between the two charges if q is located 0.50 m from the surface of Q. 8. _________________ 9. Find the electric force between the two charges if q is moved onto the surface of Q. 9. _________________ 10. If the mass of q is 0. 125 g what is its initial acceleration if released from this new position? 10. ________________ A +15 µC charge is located in free space. 11. Find the electric field strength 0.50 m from the charge. 11. ________________ 12. Find the force acting on an electron that is 0.50 m from the charge. Is it attractive, or is it repulsive? 12. ________________ 40 Two charges of -0.48 C each are located at opposite corners of a square having a side of 0.0125 m. 13. Find the electric field strength at the center of the square. 13. ________________ 14. Find the electric field strength at one of the unoccupied corners. 14. ________________ The following question is about sketching electric field lines. 15. Charge A is +8 C, charge B is -4 C, charge C is +4 C and charge D is -8 C. Assume the charges are far enough apart that their fields do not affect one another. Sketch in the electric field lines about all four charges so that their densities are correct relative to one another. 15. ____In figure_____ A charge of q = +75.0 µC and m = 0.025 g is moved from Plate A, having a voltage (potential) of 0.0 V to Plate B, having a voltage (potential) of 175.0 V. The distance from A to B is 0. 25 cm. 16. Sketch in the electric field lines, both in between the plates, and partially outside them. 16. __In figure___ 17. What is the potential difference undergone by the charge? 17. ________________ 18. What is the work done in moving the charge from A to B? Express your answer in both J and eV. 18. _______________________ 19. What is the magnitude of the electric field between the plates? 19. ________________ 20. What is the acceleration of the charge q? Ignore the weight of the charge. 20. ________________ Suppose the current in a 2.25 mm diameter copper wire is 1.50 A is used to light a bulb, and the number density of the free electrons in the metal of the wire is 2.25´1026 m-3. 21. Find the drift velocity of the electrons. 21. ________________ 22. How long would it take an electron with this drift velocity to travel 2.50 m from an on-off switch through a wire to the bulb? 22. ________________ 23. Explain, then, why the bulb lights up immediately when the switch allows the current to begin flowing. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 41 Topic 5.2 – Heating effect of electric circuits Summative Assessment v1 NAME: _____________________________________ PERIOD: __ LEVEL: ____ THIS ASSESSMENT COUNTS AS EVIDENCE! Show formulas, substitutions, answers (in spaces) and units! A carbon-core resistor consists of a carbon rod having a length of 9.75 mm, a diameter of 0.0150 mm and a resistivity of 3500´10-8 W m. 1. What is the value of the cross-sectional area of the carbon rod. Be sure your answer is in m2. 1. _________________ 2. What is the resistance of the carbon rod? 2. _________________ 3. If a current of 1.25 A passes through the resistor, what is the voltage across the resistor? 3. _________________ An unknown material has the V-I characteristics shown in the graph. 4. What is the resistance of the material when the current is 0.2 mA? 4. _________________ 5. What is the resistance of the material when the current is 0.7 mA? 5. _________________ 6. What is the resistance of the material when the voltage is 1.5 V? 6. _________________ 7. Is this material ohmic? Explain. ________. _________________________________________. A voltmeter records the displayed potential difference when the leads are placed across a 1200 W resistor. 8. What is the current passing through the resistor? 8. _________________ 9. How much charge passes through the resistor in exactly 2.5 minutes? 9. _________________ 10. How much electrical energy is required to pass the charge you found in (8) through the resistor? 10. ________________ 11. What is the fractional error in the voltage measurement? A filament lamp has a rating of 1.75 W. While the bulb is lit, the meter displays the value shown. 12. What is the power dissipation of the lamp? 12. ________________ 13. What is the current in the lamp? 13. ________________ 14. What is the resistance of the lamp? 14. ________________ 42 11. ________________ A series circuit powered by a 5.0 V cell is shown. 15. What is the total or equivalent resistance of this circuit? 15. ________________ 16. What is the current through this circuit? 16. ________________ 17. What are the voltages across each resistor? 17. V1 = _____________ V2 = ____________ V3 = ____________ A parallel circuit powered by a 5.0 V cell is shown. 18. What is the total or equivalent resistance of this circuit? 18. ________________ 19. What is the current through the cell? X 19. ________________ 20. What are the currents through each resistor? 20. I1 = _____________ I2 = _____________ I3 = _____________ 21. What is the current through the point X? 21. ________________ A series circuit powered by a battery whose voltage is 8.0 V is shown in the schematic diagram. 22. Label VOUT and VIN in this circuit. 22. __In diagram___ 23. Suppose the value of R1 is 1600 W. If we would like to “tap” 2.0 V at VOUT what should the value of R2 be? 23. ______________ 24. Suppose the value of R2 is 1600 W. If we would like to “tap” 2.0 V at VOUT what should the value of R1 be? 24. ______________ 25. What is this type of circuit called? 25. _____________________ A combination circuit powered by a 5.0 V cell is shown. 26. What is the total or equivalent resistance of this circuit? 26. _____________ 27. What is the current in R1? 27. _____________ 28. What is the voltage across R1? 28. _____________ 29. What are V2 and V3? 29. V2 =____________ V3 =____________ 30. What are I2 and I3? 30. I2 =_____________ I3 =_____________ 43 Topic 5.3 – Electric cells Summative Assessment v1 NAME: _____________________________________ PERIOD: __ LEVEL: ____ THIS ASSESSMENT COUNTS AS EVIDENCE! Show formulas, substitutions, answers (in spaces) and units! The following questions are about chemical cells. 1. Explain why a chemical cell would use two different types of metal for its terminals, rather than one type. _____________________________________________________________________________ __________________________________________________________________________. 2. Who was it that is responsible for our using “conventional current” rather than electron current? 2. ____________________________. 3. Sketch and label a chemical cell that uses electron current, and one that uses conventional current. Explain for each of them how the cell makes the charge move. Explain for each of them where the charge has the higher potential. __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ __________________ ________________ ______________________________________ ___________________________________ ______________________________________ ___________________________________ ______________________________________ ___________________________________ ______________________________________ ___________________________________ The following questions are about primary and secondary cells. 4. What is a primary cell? _________________________________________________________. 5. What is a secondary cell? _______________________________________________________. 6. Label each battery/cell with its correct designation: Primary or secondary, cell or battery. _________________ ___________________ ___________________ The following question is about changing the potential energy of charges through battery usage. 7. A 475 µC of charge is brought from an electric potential of 12.75 V to an electric potential of 5.50 V through use of a battery. What is the change in potential energy of the charge? 44 7. _________________ Suppose you measure the unloaded p.d. of one of the cells of your calculator to be 1.56 V. Then, while a 3200. W resistor is connected across the terminals of the same cell, you measure the loaded p.d. of the cell to be 1.48 V. 8. What is the emf of the cell? 8.__________________ 9. What is the terminal voltage of the cell under the load? 9.__________________ 10. What is the internal resistance of the cell under this load? 10._________________ A car battery has a terminal voltage of 14.5 V with no load. While the 8.25 W starter is engaged the battery’s terminal voltage drops to 8.75 V. 11. What is the current drawn by the starter? 11._________________ 12. What is the internal resistance of the battery? 12._________________ 13. What is the power delivered by the emf of the battery during the starting of the car? 13._________________ A cell has an unloaded potential difference of 3.20 V. A 250.4 W resistor is connected as a load as shown in the picture. The meter shows the new p.d. 14. What is the emf of the cell? 14. ______________ 15. What is the current through the resistor? 15. ______________ 16. What is the internal resistance of the battery? 16. ______________ 17. Explain what emf stands for, and in words, what in general is the emf of a cell? ________________________. ________________________________________________. 18. What is the rate at which heat is being produced in the in the 250.4 W resistor? 18._________________ 19. What is the rate at which heat is being produced in the battery? 19._________________ 20. What is the rate at which chemical energy is being converted to electrical energy in the cell? 20._________________ 45 Topic 1.1 – Measurements in physics Formative Assessment NAME: _________________________________ TEAM:__ 46 Topic 5.4 – Magnetic fields Summative Assessment v1 NAME: _____________________________________ PERIOD: __ LEVEL: ____ THIS ASSESSMENT COUNTS AS EVIDENCE! Show formulas, substitutions, answers (in spaces) and units! 1. State the pole law, and compare and contrast it with the charge law. _________________________ _________________________________________________________________________________ _________________________________________________________________________________ ________________________________________________________________________________. 2. Sketch in a compass needle pictured bar magnet. at the labeled points surrounding the 2.__In figure___ 3. Compare and contrast a magnetic dipole and an electric dipole. Include a sketch of both. __________________________________________________ ______________________________________________________________ _____________________________________________. 4. The current is traveling from left to right in the wire pictured here. Using dots and ´s, sketch in the magnetic field surrounding the wire. What happens to the field when the current is turned off? Explain how the right hand rule works. _____________ ________________________________________________________________________________ ________________________________________________________________________________ __________________________________________________________________________. 5. A magnetic field created by a current in a straight wire surrounds the wire as shown. State the direction of the current, and explain how the right hand rule works. ______________. ______________________ _________________________________________________________________________________ __________________________________________________________________________. 6. What is the strength of the magnetic field 2.25 cm from the wire if the current is 240. A? 6.__________________ 7. What is the strength of the magnetic field at the center of a loop having a radius of 2.25 cm if the current is 240. A? 7.__________________ 8. Sketch the magnetic field lines in the solenoid shown here. Assume the current enters on the right and exits on the left. Explain how the right hand rule works. _____________________________________________________________________ _____________________________________________________________________ _______________________________________________________________. 47 9. A straight wire is located in an external magnetic field as shown to the right. If a current is directed downward through the wire, which way will the magnetic force cause the wire to curve? Why? ____________. _______________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _____________________________________________________________. 10. A current-carrying loop of wire is placed in a uniform external magnetic field as shown. If the current in the wire is traveling counterclockwise in the picture, what do you predict the loop will do when released? Why? ________________________ ____________________________________________________________________ ____________________________________________________________________ __________________________________________________________________________. 11. A -2.50 µC charge having a velocity of 7.50´106 ms-1 enters an external magnetic field having a magnetic flux density of 0.225 T. Find the magnitude of the magnetic force acting on the charge as it is in the field. Sketch in the direction that the charge will follow as it passes through the field. Explain how the right hand rule works. What will its speed be when it exits the field? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ __________________________________________________________________________. 12. If the current in the 25-cm long wire of problem 9 is 1.75 A, and the magnetic field strength is 0.35 T, find the magnitude and the direction of the magnetic force acting on the wire. 12.________________ 13. An electron enters a region of magnetic field as shown. Which way will it be deflected? 13. ______________ 14. The diagram shows three parallel wires P, Q, and R, each having the same current I. The resultant force on wire R due to wire P and wire Q is A. perpendicular and into the plane of the paper. B. perpendicular and out of the plane of the paper. C. in the plane of the paper and to the right. D. in the plane of the paper and to the left. 48 Additional Topic 5 questions Measurement and uncertainties 1 ? Test yourself 5.1 Electric fields 1 Four equal charges q = −5.0 µC are placed at the vertices of a square of side 12 cm, as in the diagram. Determine the force on the charge at the top right vertex. 6 The potential difference between consecutive dotted lines in the diagram is 50 V. The red arrows indicate the electric field. 50 V A 50 V B C electric field E 2 A small plastic sphere is suspended from a fine insulating thread near, but not touching, a large sphere that is being charged. As the charge on the big sphere increases it is observed that i the plastic sphere is slowly attracted toward the large sphere, ii eventually touching it, iii at which point it is violently repelled. Carefully explain these observations. 3 The electric field at a point in space has magnitude 100 N C−1 and is directed to the right. An electron is placed at that point. For this electron, calculate a the force and b the acceleration. 4 The number of electrons per second moving through the cross-sectional area of a copper wire is 4.0 × 1019. a Determine the current in the wire. b The diameter of the wire is 1.5 mm and the number of free electrons per unit volume for copper is 8.5 × 1028 m−3. Estimate the drift speed for the electrons. 5 Give an estimate for the number of free electrons per unit volume for gold (density 19 390 kg m−3; molar mass 197 g mol−1). Assume that each atom contributes just one electron to the set of free electrons. a Calculate the work that must be done by an external agent in moving a charge of +5.0 µC from A to B. b Repeat the calculation in a when the same charge is moved from A to C. c The +5.0 µC charge is moved from A to C and then from C to B. Calculate how much work would be required then. Compare your answer to that in part a and comment. d An electron is released from rest from a point on line B. State whether the electron will reach line A or line C and calculate its speed there. 7 a An electron is accelerated by a potential difference of 100.0 V. Determine the speed of the electron after acceleration. b Determine the speed a proton would attain if accelerated by the same potential difference as the electron. 8 Two positive point charges of magnitude q and 9q are a distance d apart, as shown in the diagram. d q d 4 9q P a Calculate the electric field strength at point P, d a distance from q. 4 b Sketch a graph of the electric field as a function of the distance x from the charge q. (Take the field to be positive if it is directed to the right.) c How do the answers to a and b change if the charges are both negative? PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY49 PRESS 2014 ADDITIONAL TOPIC 5 QUESTIONS 1 17 Determine the resistance between A and B in the diagram. 5.2 Heating effect of electric currents 9 Explain why a light bulb is most likely to burn out when it is first turned on rather than later. 10 State the factors that affect the resistance of a metal wire. 11 Determine the factor by which the resistance of a wire changes when its radius is doubled. 12 The resistance of a fixed length of wire of circular cross-section is 10.0 . Predict the resistance of a wire of the same length made of the same material but with only half the radius. 13 Look at the arrangement of resistors shown in the diagram. 3.0 Ω 1.0 Ω 2.0 A 4.0 Ω 1.0 A 4.0 Ω A 9.0 Ω B a Find the current in, and potential difference across, each resistor. The potential at A is 12 V. b What is the potential difference between A and B? 14 A light bulb is rated as 60 W at 220 V. a Calculate the current flows in the light bulb when it is connected in series to a 220 V source of voltage. b The lamp is connected in series to a 110 V source of voltage. Calculate the current flows in the lamp. (Assume the resistance stays the same.) c Determine the power output of the light bulb when it is connected to the 110 V source. 15 Determine the energy used when a 1500 W kettle is used for four minutes: a in kW h b in joules. 16 In country X the voltage supplied by the electricity companies is 110 V and in country Y it is 220 V. Consider a light bulb rated as 60 W at 110 V in X and a light bulb rated as 60 W at 220 V in Y. Take the cost of electricity per kW h to be the same. Suggest where it costs more to operate a light bulb for one hour. 2 ADDITIONAL TOPIC 5 QUESTIONS A 10.0 Ω 20.0 Ω 30.0 Ω B 10.0 Ω 10.0 Ω 20.0 Ω 18 Six light bulbs, each of constant resistance 3.0 , are connected in parallel to a battery of emf = 9.0 V and negligible internal resistance. The brightness of a light bulb is proportional to the power dissipated in it. Compare the brightness of one light bulb when all six are on, to that when only five are on, the sixth having burnt out. 19 One light bulb is rated as 60 W at 220 V and another as 75 W at 220 V. a Both of these are connected in parallel to a 110 V source. Determine the current in each light bulb. (Assume that the resistances of the light bulbs are constant.) b Would it cost more or less (and by how much) to run these two light bulbs connected in parallel to a 110 V or a 220 V source? 20 Three appliances are connected (in parallel) to the same outlet, which provides a voltage of 220 V. A fuse connected to the outlet will blow if the current drawn from the outlet exceeds 10 A. The three appliances are rated as 60 W, 500 W and 1200 W at 220 V. Suggest whether the fuse blows. 21 An electric kettle rated as 1200 W at 220 V and a toaster rated at 1000 W at 220 V are both connected in parallel to a source of 220 V. The fuse connected to the source blows when the current exceeds 9.0 A. Determine whether both appliances can be used at the same time. 22 At a given time a home is supplied with 100.0 A at 220 V. How many 75 W (rated at 220 V) light bulbs could be on in the house at that time, assuming they are all connected in parallel? PHYSICS FOR 50 THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2014 23 a Determine the reading of the voltmeter in the circuit shown in the diagram if both resistances are 200 and the voltmeter also has a resistance of 200 . b Determine the reading of the ammeter. c The voltmeter is replaced by an ideal voltmeter. Determine the readings of the voltmeter and ammeter. 12.0 V R A R 26 State the reading of the ideal voltmeter in the circuit in the diagram. 6.0 V V 27 Two resistors are connected in series as shown in the diagram. The cell has negligible internal resistance. Resistor R has a constant resistance of 1.5 Ω. V R 24 For the circuit shown in the diagram, calculate the current taken from the supply. ԑ = 120 V 40 Ω 80 Ω X The current–voltage (I–V ) characteristic of resistance X is shown in the diagram. The potential difference across resistor R is 1.2 V. Calculate the emf of the cell. I /A 1.4 1.2 12 Ω 120 Ω 25 Two identical lamps are connected to a cell of emf 12 V and negligible internal resistance, as shown in the diagram. Calculate the reading of the (ideal) voltmeter when lamp B burns out. 1.0 0.8 0.6 0.4 0.2 12 V V/V 0.0 0 1 2 3 4 V A B PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY51 PRESS 2014 ADDITIONAL TOPIC 5 QUESTIONS 3 28 A lamp of constant resistance operates at normal brightness when the potential difference across it is 4.0 V and the current through it is 0.20 A. To light up the lamp, a student uses the circuit shown in the diagram. 8.0 V 60 Ω 60 Ω 28 Two light bulbs are rated as 60 W and 75 W at 220 V. If these are connected in series to a source of 220 V, what will the power in each be? Assume a constant resistance for the light bulbs. 29 A device D, of constant resistance, operates properly when the potential difference across it is 8.0 V and the current through it is 2.0 A. The device is connected in the circuit shown, in series with an unknown resistance R. Calculate the value of the resistance R. (The cell has negligible internal resistance.) emf 12 V a Calculate the resistance of the light bulb at normal brightness. b Calculate the potential difference across the light bulb in the circuit in the diagram. c Calculate the current through the light bulb. d Hence explain why the light bulb will not light. 24 Each resistor in the diagram has a value of 6.0 . Calculate the resistance of the combination. 25 You are given one hundred 1.0 resistors. Determine the smallest and largest resistance you can make in a circuit using these resistors. 26 A wire that has resistance R is cut into two equal pieces. The two parts are joined in parallel. What is the resistance of the combination? 27 A toaster is rated as 1200 W and a mixer as 500 W, both at 220 V. a Both appliances are connected (in parallel) to a 220 V source. Determine the current in each appliance. b How much energy do these appliances use if both work for 1 hour? 4 ADDITIONAL TOPIC 5 QUESTIONS R D 35 Twelve 1.0 resistors are placed on the edges of a cube and connected to a 5.0 V battery, as shown in the diagram. Determine the current leaving the battery. ε = 5.0 V PHYSICS FOR 52 THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2014 5.3 Electric cells 5.4 Magnetic fields 36 A direct current supply of constant emf 12.0 V and internal resistance 0.50 Ω is connected to a load of constant resistance 8.0 . Find: a the power dissipated in the load resistance b the energy lost in the internal resistance in 10 min. 37 Two identical lamps, each of constant resistance R, are connected as shown in the circuit on the left. A third identical lamp is connected in parallel to the other two. 39 An electron is shot along the axis of a solenoid that carries current. Suggest whether it will experience a magnetic force. 40 The diagram shows four different wires carrying current and the magnetic force on each. Determine the direction of the magnetic field in each case. ε ε I F F a A A b 60.0 Ω ε = 12.0 V r = 3.0 Ω F c d conductor 2 I z B field 20.0 Ω 60.0 Ω I into page 42 A proton of velocity 1.5 × 106 m s–1 enters a region of uniform magnetic field B = 0.50T. The magnetic field is directed vertically up (along the positive z-direction) and the proton’s velocity is initially on the z–x plane, making an angle of 30° with the positive x-axis. 57.0 Ω 40.0 Ω I out of page 41 The diagram shows two parallel conductors carrying current out of the page. Conductor 1 carries double the current of conductor 2. On a copy of the diagram, draw to scale the magnetic fields created by each conductor at the position of the other and the forces on each conductor. conductor 1 2I Compare the brightness of lamp A in the original circuit (left) with its brightness in the circuit with three lamps (right), when: a the battery has no internal resistance b the battery has an internal resistance equal to R. 38 Find the current in each of the resistors in the circuit in the diagram. What is the total power dissipated in the circuit? I F y x a Show that the proton will follow a helical path around the magnetic field lines. b Calculate the radius of the helix. c Determine the number of revolutions per second the proton makes. d Determine the velocity of the proton along the field lines. e Calculate the vertical separation of the coils of the helix. PHYSICS FOR THE IB DIPLOMA © CAMBRIDGE UNIVERSITY53 PRESS 2014 ADDITIONAL TOPIC 5 QUESTIONS 5 43 An electron enters a region of uniform magnetic field B = 0.50T. Its velocity is normal to the magnetic field direction. The electron is deflected into a circular path and leaves the region of magnetic field after being deflected by an angle of 30° with respect to its original direction. Determine the time for which the electron was in the region of magnetic field. 44 Two identical charged particles move in circular paths at right angles to a uniform magnetic field as shown in the diagram. The radius of particle 2 is twice that of particle 1. Determine the following ratios: period of particle 2 a period of particle 1 E of particle 2 b K EK of particle 1 particle 2 region of magnetic field into page particle 1 2R R 6 ADDITIONAL TOPIC 5 QUESTIONS PHYSICS FOR 54 THE IB DIPLOMA © CAMBRIDGE UNIVERSITY PRESS 2014 10 Two long parallel wires carry equal currents in opposite directions. What field do the two wires produce at point M, which is midway between the wires and on the plane of the paper? M A B C D a magnetic field parallel to the wires an electric field parallel to the wires a magnetic field at right angles to the plane of the page an electric field at right angles to the plane of the page 11 A student assigns currents at a junction in a circuit as shown in the diagram. I1 I3 I2 The student’s calculations correctly give that I1 = 3 A and I2 = −2 A. The value of I3 is: A B C D 1A −1 A 5A −5 A 12 The graph shows the variation with voltage V across a filament lamp with the current I though the lamp. I / mA 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 V/V a Suggest whether the resistor obeys Ohm’s law. b Calculate the resistance of the lamp when V = 4.0 V. c The resistivity of the filament of the lamp at a voltage of 4.0 V is 3.0 × 10−7 m. The radius of the filament is 0.25 mm. Calculate the length of the filament. [1] [2] [2] 5 ELECTRICITY AND MAGNETISM 55 245 d Two lamps whose I–V characteristics are given by the graph above are connected in parallel to a battery of negligible internal resistance. The current leaving the battery is 2.0 mA. Estimate: i the emf of the battery [1] ii the power dissipated in each lamp. [1] e Thermal energy is generated in a filament lamp when it is operating. Describe the mechanism by which this energy is generated. [3] 13 The three devices in the circuit shown are identical and may be assumed to have constant resistance. Each device is rated as 1500 W at 230 V. The emf of the source is 230 V and its internal resistance is negligible. ԑ S1 S2 a Calculate the resistance of one of the devices. b Calculate the total power dissipated in the circuit when: i S1 is closed and S2 is open ii S1 is closed and S2 is closed iii S1 is open and S2 is open iv S1 is open and S2 is closed. c In the circuit below the cell has internal resistance 0.0500 . When the switch in series with a motor of resistance of 25.0 is open, the voltmeter reads 11.5 V and the current in the ammeter is 9.80 A. [2] [1] [1] [1] [1] V M A The switch is closed. i Determine the emf of the cell. ii State and explain the effect, if any, of closing the switch on the brightness of the lamp. iii Calculate the current through the motor. 246 56 [2] [2] [2] 14 A current I is established in the conductor. The diagram shows one of the electrons making up the current moving with drift speed v. The conductor is exposed to a magnetic field B at right angles to the direction of motion of the electron. d v B a On a copy of the diagram, draw an arrow to indicate the direction: i of the conventional current in the conductor ii the magnetic force on the electron. b Show that the current in the conductor is given by I = qnAv, where q is the charge of the electron, A the cross-sectional area of the conductor, v the drift speed of the electrons and n is the number of free electrons per unit volume. c Explain why a potential difference will be established between the top (T) and bottom (B) faces of the conductor. d i The electric field between T and B is given by E = Vd where V is the potential difference between T and B and d is their separation. Show that the voltage between T and B (the Hall voltage) is given by V = vBd. ii The current in the conductor is 0.50 A, the number density of electrons is 3.2 × 1028 m−3, the crosssectional area of the wire is 4.2 × 10−6 m2 and the magnetic field is 0.20 T. Calculate the Hall voltage in this conductor. e Outline how the existence of the Hall voltage can be used to verify that the charge carriers in the conductor are negatively charged. [1] [1] [3] [3] [2] [3] [2] 15 A proton of mass m and electric charge q enters a region of magnetic field at point X and exits at point Y. The speed of the proton at X is v. The path followed by the proton is a quarter of a circle. X Y 5 ELECTRICITY AND MAGNETISM 57 247 a State and explain whether the speed of the proton at Y is the same as the speed at X. b Suggest why the path of the proton is circular. c i Show that the radius of the circular path is given by R = mv qB , where B is the magnetic flux density. ii The speed of the proton is 3.6 × 106 m s−1 at X and the magnetic flux density is 0.25 T. Show that the radius of the path is 15 cm. iii Calculate the time the proton is in the region of the magnetic field. d i The proton is replaced by a beam of singly ionised atoms of neon. The ions have the same speed when they enter at X. The beam splits into two beams: B1 of radius 38.0 cm and B2 of radius 41.8 cm. The ions in beam B1 have mass 3.32 × 10−26 kg. Predict the mass of the ions in beam B2. ii Suggest the implication of d i for nuclear structure. [2] [2] [2] [2] [2] [2] [2] 16 In the circuit shown A, B and C are three identical light bulbs of constant resistance. The battery has negligible internal resistance. a Determine the order of brightness of the light bulbs. b Bulb C burns out. Predict how the brightness of A will change. c Bulb C operates normally, but now bulb B burns out. Compare the brightness of A and of C now to the brightness they had before B burnt out. A [2] [2] [2] B C 17 Consider the circuit shown in which the batteries are assumed to have negligible internal resistance. 4.0 Ω 4.0 Ω A 4.0 Ω 2.0 V 4.0 V 4.0 V B a Calculate the current, magnitude and direction, in each battery. b Determine the potential difference between points A and B. c Determine the total power in each battery, commenting on your answer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opic 5: Electricity and magnetism Topic 5: Electricity and magnetism 1. Two identical spherical conductors X and Y are mounted on insulated stands. X carries a charge of +8.0 nC and Y carries a charge of 2.0 nC. +8.0nC 2.0nC conductor X conductor Y insulated stands The two conductors are brought into contact and are then separated. Which of the following gives the charge on each conductor? Charge on X Charge on Y A. 0.0 nC 0.0 nC B. +8.0 nC 2.0 nC C. +5.0 nC +5.0 nC D. +3.0 nC +3.0 nC (1) 2. The diagram below shows a positively charged rod brought near an isolated uncharged metal plate. + + ++ + + ++ rod plate As a result of bringing the rod near to the plate, A. the metal plate will gain a charge dependent on the separation of the rod and the plate. B. the metal plate will remain uncharged. C. the metal plate will gain a negative charge. D. the metal plate will gain a positive charge. (1) 3. An isolated, uncharged metal conductor is brought close to a positively charged insulator. ++++ ++++ insulating handle insulator conductor 1 82 Topic 5: Electricity and magnetism The conductor is earthed (grounded) for a short time and then the insulator is removed. Which of the following best represents the charge distribution on the surface of the conductor as a result of these actions? A. — — — — — B. —— — — — — — — — — — C. D. (1) 4. X and Y are two identical conducting spheres separated by a distance d. X has a charge +6 μC and Y has a charge 2 μC. The electric force between them is + F (ie attractive). The spheres are touched together and are then returned to their original separation d. The force between them now is A. +F. B. C. F. F . 3 D. F . 3 (1) 5. Three equal point charges X, Y and Z are fixed in the positions shown. Z q3 1.0 m X 90q 1.0 m q1 q2 Y The distance between q1 and q2 and the distance between q2 and q3 is 1.0 m. The electric force between the charges at X and Y is F. The electric force between the charges at X and Z is A. F . 2 B. F 2 . C. F. D. 2F. (1) 6. The electric field strength at a point may be defined as A. the force exerted on unit positive charge placed at that point. B. the force per unit positive charge on a small test charge placed at that point. C. the work done on unit positive charge to move the charge to that point from infinity. D. the work done per unit positive charge to move a small test charge to that point from infinity. (1) 2 83 Topic 5: Electricity and magnetism 7. Two positive point charges P and Q are held a certain distance apart. X P Q Y + Z + At which point(s) could the electric field strength, due to the charges, be zero? A. X only B. Y only C. Z only D. X and Z only (1) 8. Two point charges of magnitude +2Q a d Q are fixed at the positions shown below. At which point is the electric field due to the two charges most likely to be zero? +2Q Q A. B. C. D. (1) 9. The diagram below shows two parallel conducting plates that are oppositely charged. + + + X + + Y The line XY is perpendicular to the plates. Which of the following diagrams shows the variation along the line XY of the magnitude E of the electric field strength between the plates? A. B. E X E Y distance X C. Y distance Y distance D. E X E Y distance X (1) 3 84 Topic 5: Electricity and magnetism 10. In the circuit below, n charge carriers pass the point P in a time t. Each charge carrier has charge q. P The current in the circuit is given by the expression A. q . t B. nq . t C. qt . n D. nqt. (1) 11. The drift velocity of the electrons in a copper wire in which there is an electric current is A. equal to the speed of light. B. close to that of the speed of light. C. of the order of a few kilometres per second. D. of the order of a few millimetres per second. (1) 12. Which one of the following is a correct definition of electric potential difference between two points? A. The power to move a small positive charge between the two points. B. The work done to move a small positive charge between the two points. C. The power per unit charge to move a small positive charge between the two points. D. The work done per unit charge to move a small positive charge between the two points. (1) 13. The electron volt is defined as A. a unit of energy exactly equal to 1.6 × 10 19 J. B. a fraction C. the energy gained by an electron when it moves through a potential difference of 1.0 V. D. the energy transfer when 1.0 C of charge moves through a potential difference of 1.0 V. 1 of the ionization energy of atomic hydrogen. 13.6 (1) 14. Which of the following is the correct value of the electronvolt, measured in SI Units? A. 1.6 × 10 19 N B. 1.6 × 10 19 J C. 9.1 × 10 31 N D. 9.1 × 10 31 J (1) 4 85 Topic 5: Electricity and magnetism 15. The graph below shows the current/voltage characteristics of a filament lamp. The resistance of the filament at 4.0 V is A. 250 . B.4 000 . C. 8 000 . D. 64 000 . (1) 16. The graph below shows the variation with voltage V of the current I in three resistors X, Y and Z. I X Y Z 0 0 V Which of the following corresponds to resistors for which the resistance increases with increasing current? A. X only B. Z only C. X and Z D. Y and Z (1) 17. Which f he f i gi ac ec ae e f Oh a ? A. The resistance of a conductor is always constant. B. The current in a conductor is always proportional to the potential difference across the conductor. C. The resistance of a conductor increases with increasing temperature. D. The resistance of a conductor is constant only if the temperature of the conductor is constant. (1) 18. The element of an electric heater has a resistance R when in operation. What is the resistance of a second heater that has a power output three times as large at the same operating voltage? A. R 9 B. R 3 C. 3R D. 9R (1) 5 86 Topic 5: Electricity and magnetism 19. In the two circuits X and Y below, each cell has an emf E and negligible internal resistance. Each resistor has a resistance R. circuit X circuit Y E E R R R The power dissipated in circuit X is P. The best estimate for the power dissipated in circuit Y is A. P . 4 P . 2 B. C. 2P. D. 4P. (1) 20. In the circuit shown below, the cell has negligible internal resistance. 2R I3 I1 R I2 Which of the following equations is correct? A. I1 = 2I2 B. I1 = 2I3 C. I2 = 2I3 D. I3 = 2I1 (1) 21. The resistors in each of the circuits shown below each have the same resistance. circuit P circuit Q circuit S Which of the following gives the circuits in order of increasing total resistance? A. P Q S B. Q P S C. S Q P D. P S Q (1) 6 87 Topic 5: Electricity and magnetism 22. In the circuit below, which meter is not correctly connected? A 1 V A 3 2 V A. 1 B. 2 C. 3 D. 4 4 (1) 23. A battery is connected in series with a resistor R. The battery transfers 2 000 C of charge completely round the circuit. During this process, 2 500 J of energy is dissipated in the resistor R and 1 500 J is expended in the battery. The emf of the battery is A. 2.00 V. B. 1.25 V. C. 0.75 V. D. 0.50 V. (1) 24. In the circ i h , he e e ha a e i a ce f 20 k a d he ba e negligible internal resistance. ha a e f f 6.0 V and 6.0 V 10 k: 20 k: V 20 k: The reading on the voltmeter is A. 2.0 V. B. 3.0 V. C. 4.0 V. D. 6.0 V. (1) 7 88 Topic 5: Electricity and magnetism 25. In which one of the circuits is it possible to vary the current in the lamp by adjusting the variable resistor? The cell has negligible internal resistance. A. B. C. D. (1) 26. A resistor of resistance 1.0 : is connected in series with a battery. The current in the circuit is 2.0 A. The resistor is now replaced by a resistor of resistance of 4.0 :. The current in this circuit is 1.0 A. A 2.0 A 1.0 : 4.0 : The best estimate for the internal resistance of the battery is A. 1.0 :. B. 2.0 :. C. 4.0 :. D. 5.0 :. (1) 27. In the circuit below, resistors X, Y and Z are connected in series with a 9.0 V supply. +9.0 V 0 3000 : 3000 : X Y Z V Resistors X and Z are fixed resistors of resistance 3000 :. The resistance of resistor Y may be varied between zero and 3000 :. Which of the following gives the maximum range of potential difference V across the resistors X and Y? A. 0 to 6.0 V B. 3.0 V to 6.0 V C. 4.5 V to 6.0 V D. 4.5 V to 9.0 V (1) 8 89 Topic 5: Electricity and magnetism 28. The Ea h ag e ic fie d a be c a ed i h ha f a ba ag e . Which of the following diagrams correctly shows the orientation of the bar magnet in this model? A. B. geographical north pole geographical north pole N S N C. S D. geographical north pole geographical north pole S N N S (1) 29. A current-carrying solenoid is placed with its axis pointing east-west as shown below. A small compass is situated near one end of the solenoid. N W E axis of solenoid S The axis of the needle of the compass is approximately 45° to the axis of the solenoid. The current in the solenoid is then doubled. Which of the following diagrams best shows the new position of the compass needle? A. B. W E C. W E W E D. W E (1) 9 90 Topic 5: Electricity and magnetism 30. A long, straight current-carrying wire is placed normal to the plane of the page. The current in the wire is into the plane of the page. Which of the following diagrams best represents the magnetic field around the wire? A. B. C. D. (1) 31. Two long, vertical wires X and Y carry currents in the same direction and pass through a horizontal sheet of card. X Y Iron filings are scattered on the card. Which one of the following diagrams best shows the pattern formed by the iron filings? (The dots show where the wires X and Y enter the card.) A. B. C. D. (1) 10 91 Topic 5: Electricity and magnetism 32. A strip of aluminium foil is held between the poles of a strong magnet, as shown below. direction of current magnet aluminium foil When a current is passed through the aluminium foil in the direction shown, the foil is deflected. In which direction is this deflection? A. Vertically downwards B. Vertically upwards C. Towards the North pole of the magnet D. Towards the South pole of the magnet (1) 33. A magnetic force acts on an electric charge in a magnetic field when A. the charge is not moving. B. the charge moves in the direction of the magnetic field. C. the charge moves in the opposite direction to the magnetic field. D. the charge moves at right angles to the lines of the magnetic field. (1) 34. The diagram below shows a charged particle about to enter a region of uniform magnetic field directed into the page. charged particle magnetic field Which of the following correctly describes the change, if any, in the kinetic energy and the momentum of the particle in the magnetic field? Kinetic energy Momentum A. Changed Changed B. Changed Unchanged C. Unchanged Changed D. Unchanged Unchanged (1) 11 92 Topic 5: Electricity and magnetism 35. The currents in two parallel wires are I and 3I in the directions shown in the diagram below. wire 1 wire 2 I 3I The magnetic force on wire 2 due to the current in wire 1 is F. The magnitude of the force on wire 1 due to the current in wire 2 is F . 3 A. B. F . 2 C. F. D. 3F. (1) 36. The diagram below shows three parallel wires P, Q and R that are equally spaced. I I I wire P wire Q wire R The currents in the wires are each of the same magnitude I and are in the directions shown. The resultant force on wire Q due to the current in wire P and in wire R is A. perpendicular and into the plane of the paper. B. perpendicular and out of the plane of the paper. C. in the plane of the paper to the right. D. in the plane of the paper to the left. (1) 37. A straight conductor is in the plane of a uniform magnetic field as shown. current I magnetic field The current in the conductor is I and the conductor is at an angle θ to the magnetic field. The force per unit length on the conductor due to the current in the magnetic field is P. Which is the correct expression for the magnitude of the magnetic field strength? A. P sin T I B. P cosT I C. P I sin T D. P I cosT (1) 12 93 Topic 5: Electricity and magnetism 38. A positively charged particle e e a egi f if ag e ic fie d. The di ec i f he a ic e velocity is parallel to the direction of the magnetic field as shown in the diagram below. region of uniform magnetic field charged particle Which of the following diagrams correctly shows the path of the charged particle while in the region of magnetic field? A. B. C. D. (1) 39. An electron is travelling in the direction shown and enters a region of uniform magnetic field. direction of travel of the electron e direction of magnetic field region of uniform magnetic field On entering the field the direction of the force acting on the electron is A. into the plane of the paper. B. out of the plane of the paper. C. towards the top of the page. D. towards the bottom of the page. (1) Short answer questions. 40. This question is about electric charge at rest. (a) Define electric field strength at a point in an electric field. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) 13 94 Topic 5: Electricity and magnetism Four point charges of equal magnitude, are held at the corners of a square as shown below. +Q 2a +Q 2a P –Q –Q The length of each side of the square is 2a and the sign of the charges is as shown. The point P is at the centre of the square. (b) (i) Deduce that the magnitude of the electric field strength at point P due to one of the point kQ charges is equal to . 2a 2 ........................................................................................................................... ........................................................................................................................... (2) (ii) On the diagram above, draw an arrow to represent the direction of the resultant electric field at point P. (1) (iii) Determine, in terms of Q, a and k, the magnitude of the electric field strength at point P. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 8 marks) 41. This question is about aspects of electric fields and electric charge. Fields and electric charge associated with atoms (a) Define electric field strength. ..................................................................................................................................... ..................................................................................................................................... (2) (b) A proton may be considered to be a point charge. For such a proton 14 95 Topic 5: Electricity and magnetism (i) sketch the electric field pattern. (2) (ii) calculate the magnitude of the electric field strength at a distance of 5.0×10 11 m from the proton. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (c) In a simple model of the hydrogen atom, an electron orbits the proton. Both electron and proton are regarded as point charges. The orbital radius of the electron is 5.0×10 11 m. (i) Using your answer to (b)(ii) deduce that the magnitude of the electric force between the electron and the proton is 9.3×10 8N. ........................................................................................................................... (1) (ii) Deduce that the kinetic energy of the electron is 2.3×10 18 J. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (iii) The total energy of the electron is 14 eV. Determine the potential energy of the electron in electron volt. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) 15 96 Topic 5: Electricity and magnetism Fields and electric charge in conductors (d) Describe the concept of drift velocity as applied to the conduction electrons in a conductor. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (e) Define electromotive force (e.m.f.). ..................................................................................................................................... ..................................................................................................................................... (1) (f) A filament lamp is operating at normal brightness. The potential difference across the lamp is 6.0 V. The current in the filament is 0.20 A. For the filament of this lamp, calculate (i) the resistance. ........................................................................................................................... ........................................................................................................................... (1) (ii) the power dissipated. ........................................................................................................................... ........................................................................................................................... (1) (g) The lamp in (f) is connected in the circuit below. The lamp is still operating at normal brightness. B R The battery B has an internal resistance of 5.0 : and the resistance R of the resistor is 15 :. 16 97 Topic 5: Electricity and magnetism (i) Calculate the current in the resistor R. ........................................................................................................................... ........................................................................................................................... (1) (ii) Determine the e.m.f. of the battery. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 25 marks) 42. This question is about forces on charged particles in electric and magnetic fields. The diagram shows two parallel plates situated in a vacuum. One plate is at a positive potential with respect to the other. + Path of positively charged particle A positively charged particle passes into the region between the plates. Initially, the particle is travelling parallel to the plates. (a) On the diagram, (i) draw lines to represent the electric field between the plates. (3) (ii) show the path of the charged particle as it passes between, and beyond, the plates. (2) (b) An electron is accelerated from rest in a vacuum through a potential difference of 750 V. (i) Determine the change in electric potential energy of the electron. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) 17 98 Topic 5: Electricity and magnetism (ii) Deduce that the final speed of the electron is 1.6 × 107 m s 1. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) The diagram below shows a cross-section through a current-carrying solenoid. The current is moving into the plane of the paper at the upper edge of the solenoid and out of the plane of the paper at the lower edge. There is a vacuum in the solenoid. Current into plane of paper ××××××××××××××××××××××××××× Current out plane of paper (c) (i) Sketch lines to represent the magnetic field inside and at each end of the solenoid. (4) (ii) A positively charged particle enters the solenoid along its axis. On the diagram, show the path of the particle in the solenoid. (1) An electron is injected into a region of uniform magnetic field of flux density 4.0 mT. The velocity of the electron is 1.6 × 107 m s 1 at an angle of 35° to the magnetic field, as shown below. (d) (i) Determine the component of the velocity of the electron normal to the direction of the magnetic field. ........................................................................................................................... ........................................................................................................................... (2) (ii) Describe, making calculations where appropriate, the motion of the electron due to this component of the velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) 18 99 Topic 5: Electricity and magnetism (iii) Determine the component of the velocity of the electron along the direction of the magnetic field. ........................................................................................................................... ........................................................................................................................... (1) (iv) State and explain the magnitude of the force on the electron due to this component of the velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (e) With reference to your answers in (d), describe the shape of the path of the electron in the magnetic field. You may draw a diagram if you wish. ..................................................................................................................................... ..................................................................................................................................... (2) (Total 25 marks) 43. This question is about electric circuits. Susan sets up the circuit below in order to measure the current-voltage (I-V) characteristic of a small filament lamp. A 3.0 V V S The supply is a battery that has an emf of 3.0 V and the ammeter and voltmeter are considered to be ideal. The a i abe ed b he a fac e a 3 V , 0.6 Wa . (a) (i) Explain what information this labelling provides about the normal operation of the lamp. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) 19 100 Topic 5: Electricity and magnetism (ii) Calculate the current in the filament of the lamp when it is operating at normal brightness. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) Susan sets the variable resistor to its maximum value of resistance. She then closes the switch S and records the following readings. Ammeter reading = 0.18 A Voltmeter reading = 0.60 V She then sets the variable resistor to its zero value of resistance and records the following readings. Ammeter reading = 0.20 A (b) (i) Voltmeter reading = 2.6 V Explain why, by changing the value of the resistance of the variable resistance, the potential difference across the lamp cannot be reduced to zero or be increased to 3.0 V. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) Determine the internal resistance of the battery. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (c) Calculate the resistance of the filament when the reading on the voltmeter is (i) 0.60 V. ........................................................................................................................... ........................................................................................................................... (1) (ii) 2.6 V. ........................................................................................................................... ........................................................................................................................... (1) 20 101 Topic 5: Electricity and magnetism (d) Explain why there is a difference between your answers to (c)(i) and (c)(ii). ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (e) Using the axes below, draw a sketch-graph of the I-V characteristic of the filament of the lamp. (Note: this is a sketch-graph; you do not need to add any values to the axes.) I 0 V 0 (1) The diagram below shows an alternative circuit for varying the potential difference across the lamp. X 3.0 V Y Z The potential divider XZ has a potential of 3.0 V across it. When the contact is at the position Y, the e i a ce f XY e a he e i a ce f YZ hich e a 12 . The e i a ce f he a i 4 . (f) Calculate the potential difference across the lamp. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 18 marks) 21 102 Topic 5: Electricity and magnetism 44. Electrical conduction In a copper wire the number of conduction electrons is equal to the number of copper atoms in the wire. (a) State what is meant by conduction electrons. ................................................................................................................................... ................................................................................................................................... (1) (b) (i) The density of copper is 8.93 × 103 kg m 3 and its molar mass is 64 g. Deduce that the number of moles of copper in a volume of 1.0 m3 is 1.4 × 105. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (ii) Estimate the number of conduction electrons in 1.0 m3 of copper. ......................................................................................................................... ......................................................................................................................... (1) (c) The diagram below shows some of the conduction electrons in a copper wire. The arrows represent the random velocities of the electrons. copper wire Explain, by reference to the motion of the electrons, why there is no current in the wire. ................................................................................................................................... ................................................................................................................................... (2) (d) An electric field is established inside the copper wire directed as shown in the diagram below. The dots represent electrons. The random velocities of the electrons are not shown. On the diagram below, draw an arrow to indicate the direction of the drift velocity of the electrons. electric field copper wire (1) 22 103 Topic 5: Electricity and magnetism (e) A typical value for the electron drift velocity in a copper wire is 10 3 m s 1. In the circuit below, the length of the copper wire joining the negative terminal of the battery to the lamp is 0.50 m. S 0.50m (i) The switch S is closed. Calculate the time it would take for an electron to move from the negative terminal of the battery to the lamp. ......................................................................................................................... ......................................................................................................................... (1) (ii) The lamp lights in a time much less than that calculated in (e)(i). Explain this observation. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (iii) Discuss, in terms of the movement of the electrons, the energy transformations taking place in the filament of the lamp. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (Total 14 marks) 45. This question is about electric circuits. (a) (i) Defi e e f a d a e Oh a . emf: .................................................................................................... .................................................................................................... Oh a : .................................................................................................... .................................................................................................... (2) 23 104 Topic 5: Electricity and magnetism (ii) The graph below shows the I-V characteristic of a particular electrical component. V 0 0 I State show the resistance of the component is determined from the graph. ......................................................................................................................... ......................................................................................................................... (1) (b) In the circuit below an electrical device (load) is connected in series with a cell of emf 2.5 V and internal resistance r. The current I in the circuit is 0.10 A. e.m.f. = 2.5V r I = 0.10A load The power dissipated in the load is 0.23 W. Calculate (i) the total power of the cell; ......................................................................................................................... ......................................................................................................................... (1) (ii) the resistance of the load; ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) 24 105 Topic 5: Electricity and magnetism (iii) the internal resistance r of the cell. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (c) A second identical cell is connected into the circuit in (b) as shown below. I = 0.15A load The current in this circuit is 0.15 A. Deduce that the load is a non-ohmic device. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (4) (Total 12 marks) 46. This question is about electrical resistance. (a) A heating coil is to be made of wire of diameter 3.5 × 10 4 m. The heater is to dissipate 980 W when connected to a 230 V d.c. supply. The material of the wire has resistivity 1.3 × 10 6 a he ki g e e a e f he hea e . (i) Define electrical resistance. ........................................................................................................................... ........................................................................................................................... (1) (ii) Calculate the resistance of the heating coil at its normal working temperature. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) 25 106 Topic 5: Electricity and magnetism (iii) Show that the length of wire needed to make the heating coil is approximately 4 m. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (b) Three identical electrical heaters each provide power P when connected separately to a supply S which has zero internal resistance. On the diagram below, complete the circuit by drawing two switches so that the power provided by the heaters may be either P or 2P or 3P. (2) (Total 7 marks) 47. (a) On the diagram below, draw the magnetic field pattern around a long straight current-carrying conductor. current-carrying wire (3) The diagram below shows a coil consisting of two loops of wire. The coil is suspended vertically. 0.20 cm 6.0 cm 26 107 Topic 5: Electricity and magnetism Each loop has a diameter of 6.0 cm and the separation of the loops is 0.20 cm. The coil forms part of an electrical circuit so that a current may be passed through the coil. (b) (i) State and explain why, when the current is switched on in the coil, the distance between the two loops changes. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) When there is a current I in the coil, a mass of 0.10 g hung from the free end of the coil returns the separation of the loops to the original value of 0.20 cm. The circumference C of a circle of radius r is given by the expression C = 2 r. (ii) Calculate the current I in the coil. You may assume that each loop behaves as a long straight current-carrying wire. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (Total 11 marks) 48. This question is about motion of a charged particle in a magnetic field. A charged particle is projected from point X with speed v at right angles to a uniform magnetic field. The magnetic field is directed out of the plane of the page. The particle moves along a circle of radius R and centre C as shown in the diagram below. region of magnetic field out of plane of page Y v R X charged particle C 27 108 Topic 5: Electricity and magnetism (a) On the diagram above, draw arrows to represent the magnetic force on the particle at position X and at position Y. (1) (b) State and explain whether (i) the charge is positive or negative; ......................................................................................................................... (1) (ii) work is done by the magnetic force. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (c) A second identical charged particle is projected at position X with a speed v in a direction 2 opposite to that of the first particle. On the diagram above, draw the path followed by this particle. (2) (Total 6 marks) 28 109

Topic 5 All questions-numbered

Related documents

Products

Support

Topic 5 All questions-numbered

Related documents

Add this document to collection(s)

Add this document to saved

Suggest us how to improve StudyLib