Gravitational Potential Energy
When in the presence of a gravitational field, a mass will have gravitational potential energy due to its position relative to the source of the force
PE = If the object had 1 J of PE at the top, what will the KE be when it hits the ground? Electric Potential (or Electric Potential Difference or Potential Difference)
Electric Potential
Electric potential energy is associated
with a charged object due to its position
relative to a source of electric force.
If the charge has 1J of PE at position A,
what will the KE be when it gets to position B?
How much work would it take to move the Charge from position B to position A?
If we consider the charge on a single electron or proton as ‘e,’ we can define a unit of energy as
1 electron­volt [eV] = V = 1. An electron falls through a potential difference of 20 V. How much work was done on the electron?
2. Convert 3.5 x 10­16 joules to electron­volts.
3. A charge of +3.0 C has 12 J of work done on it. Through what potential difference was the charge moved?
4. 45 joules of work are done in moving an object with a charge of ­3.0 x 10­6 coulombs toward a negatively charged plate.
a. Calculate the change in electrical potential (voltage) of the object after it is moved.
b. A constant force will be needed to keep the charge where it is. If the object were released, how much kinetic energy would it gain?
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5. An object with a charge of ­2.0 coulombs requires 10.0 joules of work to move it from point A to point B through an electric field. Calculate the potential difference (voltage) between points A and B. 7. An electric field is used to accelerate an electron, changing its electrical potential (voltage) by 100 volts. a. Calculate the kinetic energy gained by the electron (in electron­volts). b. Convert this measurement into joules. c. Using this energy in joules and the mass of an electron, calculate the speed of the electron. 6. 5.0 electron­volts of energy are used to move a single electron through an electric field. Calculate the change in electrical potential (voltage) for this electron. 8. A 0.005 kilogram object with a charge of 2 x 10­5 coulombs is positioned in an electric field so that it has an electrical potential of 1.5 volts. The charged body is released so that it is free to move. a. How much kinetic energy will the object gain after it is released? b. What maximum velocity will this object reach? Electric Current – “Flow of Charges”
When the ends of an electric conductor are at different electric potentials (when there is a potential difference), charges flow from the higher potential to the lower potential end. Like water flowing down a hill.
In a metal conductor, flowing electrons make up that current.
9. An object with an excess of 5 electrons is accelerated through an electric field so that it loses 15 volts of electrical potential. a. How much kinetic energy (in eV) does this object gain during this process? b. Convert this energy into joules 10. 100 Coulombs of charge pass through a wire every 4 seconds. What is the current in the wire?
Electric Current: I = ­4 seconds. What is the 11. During a thunderstorm, a lightning strike transfers 15 coulombs of charge in 1 x 10
average current produced in the strike?
Units: 1 Ampere or Amp (A) = 2
12. a) A wire carries a current of 50 amperes. How much charge passes through the wire in 10 seconds?
b) How many electrons pass through the wire every 10 seconds?
Electrical Resistance
Electrical resistance is the opposition to the flow of current through a conductor.
Resistance depends on 4 things.
1.Length of the wire
2.Cross­sectional area (wire thickness)
3.Type of material
4.Temperature
Resistance R = 19 electrons flow 13. An aluminum wire is connected to a voltage source. While it is connected 2.5 x 10
through the wire every second. a) Calculate the total amount of charge flowing through the wire in one second.
b) Calculate the electrical current in the wire in amperes.
Units: 2?
14. What is the resistance of a piece of copper wire with a length of 1 meter and a cross sectional area of 0.01 m
7 meters long and has a cross­
15. What is the composition of a wire with a resistance of 31.8 Ohms if it is 5 x 10
sectional area of 0.025 m2?
­4 meter.
16. A 14 gauge aluminum wire has a radius of 8.0 x 10
a. Calculate the cross sectional area of the wire.
b. Calculate the resistance of the wire if it is 30.0 meters long.
­6 meter has a resistance of 300 18. A 0.02 meter long carbon resistor with a cross sectional area of 2 x 10
ohms.
a. What would its resistance be if its length were doubled?
b. What would its resistance be if its cross­sectional area were tripled?
­6 meter2 has a resistance of 3.05 ohm.
17. A 500 meter long wire with a cross­sectional area of 4 x 10
Calculate the resistivity of the wire then determine the wire’s composition.
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Circuits
A circuit is a closed path in which current flows. Typically circuits are described in terms of current, voltage, and resistance.
Current – The flow of charge – I = Ohm’s Law
R = Voltage – Potential Energy per unit charge, “Electrical Pressure” – V = Resistance – The resistance to the flow of charge – R = If resistors resist the flow of charge, then more resistance would lead to _______________ current and vice versa. Current and resistance have a(n) _______________ relationship.
If you want to push the same amount of current through greater resistance, then you must ___________
the voltage (or “electrical pressure”). Voltage and resistance have a(n) _____________ relationship.
Problems:
21. The voltage supplied to a circuit with a resistance of 100 ohms is 25 volts. How much current will flow in this circuit?
22. A current of 2 amperes flows through a circuit with a resistance of 10 ohms. What is the voltage supplied to the circuit?
23. A 10 volt battery is connected to a circuit, allowing 5 amperes of current flow. Calculate the resistance of the circuit.
24. A 12 volt battery sends 30 coulombs of charge through a light bulb every 6 seconds. a) Calculate the current going through the light bulb
b) Calculate the resistance of the light bulb
­6 square meter.
25. A 100.­meter length of copper wire with a cross­sectional area of 3.0 × 10
a) What is the resistance of the wire?
b) How much current will flow through the wire?
26. 10 coulombs of charge have 90 joules of potential energy in a circuit. The 10 coulombs pass through the circuit once every 2 seconds.
a) What is the potential difference in the circuit?
b) What is the current in the circuit?
c) What is the resistance in the circuit?
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Circuit Diagrams
A circuit is a closed path in which current exists.
DC = Direct Current
AC = Alternating Current
A cell or battery provide the circuit with a constant potential difference (or voltage)
A switch (like a light switch) can open or close a circuit, or can change a circuit
A voltmeter measures potential difference (Volts)
An ammeter measures current (Amps)
A resistor resists the flow of charge. A variable resistor can change its resistance.
A lamp is a type of resistor which lights up when current flows through it.
We will treat the wire between resistors as having zero resistance
Circuit 1
A 12 Volt battery is connected to a 4 Ohm resistor. What is the current
through the resistor?
Circuit 2
Draw a 1.5 Volt cell connected to a variable resistor. At what resistance value (in Ohms) would you want to set the resistor such that the current is 0.6 A?
Circuit 3
What is the current through this circuit when the switch is closed?
What is the current through this when the switch is open? Why?
Calculate the current for both circuits. What is the difference between the circuits?
Valid vs Invalid Circuits
A circuit must make at least one complete loop (including the voltage source). If a circuit does not make a loop, current cannot flow.
Circuit 6
Draw a circuit with a 9 V battery supplying 4.5 Coulombs per second of current to a lamp. What is the resistance of the lamp?
What is a short circuit?
A short circuit occurs when there is (at least) one path in a circuit with zero (or near­zero) resistance. Since there is no resistance, the current flow approaches:
Short circuits are not valid either.
Circuit 7
Draw a circuit with a cell providing 3 Amps of current to a lamp with 2 Ohms of resistance. How much voltage is the cell providing?
Should switch A be open or closed?
Should switch B be open or closed?
Should switch C be open or closed?
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Electrical Power
Electric Potential Difference – 1 Volt = Power in Circuits depends on:
How much energy each unit of charge has ­> ____________
More ____________ means more energy per Coulomb ­> ____________ power
As electrons travel through circuits, they do work. How much potential energy does each Coloumb of charge have in a 1V battery?
How much work can each Coulomb of charge do in a 1V battery?
How many electrons are flowing through it ­> ____________
Recall, Power = More ____________ means more charge means ­>____________ power
Power = How does a light bulb work?
Believe it or not, Thomas Edison did not invent the light bulb. 33. What is the power generated in a circuit that conducts 10A of current when connected to a 15V battery?
When electric potential (voltage) is applied to a circuit, and there is resistance in the circuit, where does that potential energy go? What do we call that?
Scientists noticed that with more resistance, wires would heat up more. So they searched for materials with greater _________________ than copper, like Tungsten. They made the filament long and very thin in order to _________________ resistance. This resistance heats the filament up to 3000 degrees Celsius! This is what causes the light bulb to glow.
34. How much current is drawn by a 800W light bulb when it is connected to a 20V power supply?
37. How much power is used by a 20 Ohm resistor connected to a 10V voltage source? Draw a diagram
35. A 100W light bulb is connected to a 12V power supply. a) Draw the circuit
b) What is the current flowing through the light bulb?
c) What is the resistance of the light bulb?
38. How much current is flowing through a 100W circuit with a 10 Ohm resistor? 36. How much work is done by an 80 W light bulb in 2 minutes?
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Series and Parallel Circuits
Objects in series follow each other along a single path
Objects in parallel follow multiple paths that run parallel to each other
Resistors in Series & Parallel
Recall:
Voltage is “electrical pressure”
Current is electrical flow
Resistors resist the flow of charge
A, B, C, and D are water pipes. Which will let water flow the easiest? Which will resist the flow of water the most? Why?
Now assume each is a wire is made of copper. Which will have the most resistance? Which will have the least? Why?
Series Circuit
In series, having resistors follow in a row is like extending the length of a single resistor. Adding resistors is like making a long thin road even longer. It will increase resistance. Which of the following roads would you prefer to be stuck on during rush hour? Which will allow the greatest number of cars to pass per hour (or current)?
Which road has the most resistance?
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For any series circuit:
Is it possible for more charge to flow through the 1.5 Ohm resistor than the 3 Ohm resistor or vice versa? No! The current must be the same flowing through all resistors in series.
Calculate the potential difference in the 1.5 Ohm resistor using Ohm’s law (R = V/I)
Calculate the potential difference in the 3 Ohm resistor using Ohm’s law.
I = V = Req = What is the potential difference for the entire circuit? Does this match up with the battery?
An 8 ohm an two 4 ohm resistors are connected in series to a 24 V power source
Complete a VIRP chart
Draw a circuit with a 3 Ohm resistor in series with a 6 Ohm resistor. The circuit is connected to an 18 V battery. Calculate the current through the 6 Ohm resistor.
A 20 ohm and 10 ohm resistor are connected to a 60V power source. Complete a VIRP chart
Parallel Circuit
Resistors in parallel is like increasing the cross­sectional area of a single resistor. It gives current more paths in which current can travel. Adding resistors in parallel is like allowing more paths for traffic to travel through. It will decrease resistance.
Voltage remains the same across each resistor. Voltage is measured across resistors, whereas current is measured through resistors.
Calculate the current through the 6 Ohm resistor (using Ohm’s Law).
Calculate the current through the 3 Ohm resistor.
How does do those currents compare to the current for the circuit? Does that make sense? A fork in the road can split traffic, but the total traffic before and after the split must be the same.
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For any parallel circuit:
Draw a circuit with a three 2 Ohm resistors in parallel. The circuit is connected to a 14 V battery. Calculate the equivalent resistance, as well as the current across one of the resistors.
I = V = Req = Measuring Current
A, B, C, and D are water pipes. Which will let water flow the easiest? Which will resist the flow of water the most? Why?
An ammeter is a device which measures current (Amps)
If you wanted to measure the traffic going down Old Country Road, would you want to put a traffic counter in series or in parallel to the road?
Now assume each is a wire is made of copper. Which will have the most resistance? Which will have the least? Why?
45. Finish the following drawing: The battery is connected to a 5 Ohm resistor and an ammeter is set up to measure current.
46. A 16 V battery is connected to a 5 Ohm resistor and a 3 Ohm resistor in series, with an ammeter set up to measure current for the circuit. Draw the circuit.
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In a parallel circuit, an ammeter can tell you the current for each individual path on the circuit.
Measuring Voltage
A voltmeter is a device which measures potential difference (Volts)
A voltmeter measures a change in potential energy per charge in a circuit. It must be connected in parallel to a component of a circuit. Voltmeters have very high resistance to not interfere with the circuit.
Voltmeter In Parallel
Ammeter stays in Series
If the current through A1 is 10 Amps, and the current through A2 is 6 Amps, what is the current through A3?
47. Draw a voltmeter connected to the 3 Ohm resistor. What will it read?
48. Draw a voltmeter connected to the 4 Ohm resistor. What will it read?
Resistance:
Current:
Voltage
49. Draw a circuit with a 1.5 V battery and a 3 Ohm resistor. Draw an ammeter and voltmeter to measure the current and voltage across that resistor. What will the ammeter and voltmeter read?
50. In the circuit represented by the diagram below, what is the reading of voltmeter V?
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52. Sketch a parallel circuit with one 30 ohm resistor, one 50 ohm resistor, and a 100 volt battery. Include an ammeter that will read the current through the 30 ohm resistor and a voltmeter that will read the voltage drop across the 50 ohm resistor
51. Calculate the equivalent resistance of the circuit
What is the equivalent resistance of the circuit?
What is the current reading of the ammeter?
What is the power of the 30.­ohm resistor?
Determine the voltage drop across the 50 ohm resistor.
Calculate the current passing through the 30 ohm resistor.
Compare the current that passed through the 30 ohm resistor to the current passing through the 50 ohm resistor.
Compare the voltage drop across the 30 ohm resistor to the voltage drop across the 50 ohm resistor.
Junction Rule
The total current (traffic) into a junction is equal to the total current (traffic) out of the junction
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