Name
Physics R
Date: ______________
Circuits
Electric Potential Energy
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 Energy
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?
______
Electric Potential (or Electric Potential Difference or Potential Difference)
“Electric Pressure”
Electric Potential
V=
If we consider the charge on a single electron or proton as ‘e,’ we can define a unit of energy as
1 electron-volt [eV] =
1. An electron falls through a potential difference of 20 V. How much work was done on the electron?
2. Convert 3.5 x 10-16 joules to electron-volts.
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 10-6 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?
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.
6. 5.0 electron-volts of energy are used to move a single electron through an electric field. Calculate the
change in electrical potential (voltage) for this electron.
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 electron-volts).
b. Convert this measurement into joules.
c. Using this energy in joules and the mass of an electron, calculate the speed of the electron.
8. A 0.005 kilogram object with a charge of 2 x 10-5 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?
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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
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.
Electric Current: I =
Units: 1 Ampere or Amp (A) =
By convention, current flows from positive to negative.
Problems:
10. 100 Coulombs of charge pass through a wire every 4 seconds. What is the current in the wire?
11. During a thunderstorm, a lightning strike transfers 15 coulombs of charge in 1 x 10-4 seconds. What
is the average current produced in the strike?
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?
13. An aluminum wire is connected to a voltage source. While it is connected 2.5 x 1019 electrons flow
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.
3
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. Cross-sectional area (wire thickness)
a=
3. Type of material
4. Temperature
Resistance
R=
Units:
Problems:
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 m2?
15. What is the composition of a wire with a resistance of 31.8 Ohms if it is 5 x 107 meters long and has
a cross-sectional area of 0.025 m2?
16. A 14 gauge aluminum wire has a radius of 8.0 x 10-4 meter.
a. Calculate the cross sectional area of the wire.
b. Calculate the resistance of the wire if it is 30.0 meters long.
17. A 500 meter long wire with a cross-sectional area of 4 x 10-6 meter2 has a resistance of 3.05 ohm.
Calculate the resistivity of the wire then determine the wire’s composition.
18. A 0.02 meter long carbon resistor with a cross sectional area of 2 x 10-6 meter has a resistance of
300 ohms.
a. What would its resistance be if its length were doubled?
b. What would its resistance be if its cross-sectional area were tripled?
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Review Questions
19. A student walks 40 m along a hallway that heads due north, then turns and walks 30 m along
another hallway that heads due east. What is the magnitude of the student’s resultant displacement?
20. A motor used 120 watts of power to raise a 15-newton object in 3.0 seconds. Through what vertical
distance was the object raised?
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 =
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.
Ohm’s Law
R=
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?
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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
25. A 100.-meter length of copper wire with a cross-sectional area of 3.0 × 10–6 square meter.
a) What is the resistance of the wire?
b) How much current will flow through the wire if connected to a 24 V battery?
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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Review Questions
27. The graph represents the relationship between speed and time for a
car moving in a straight line. What is the magnitude of the car’s acceleration?
28. A 45-kilogram boy is riding a 15-kilogram bicycle
with a speed of 20 meters per second. What is the
combined kinetic energy of the boy and the bicycle?
29. Oil drips at 0.4 second intervals from a car that has an oil leak. Which
pattern best represents the spacing of oil drops as the car accelerates uniformly from rest?
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?
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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?
Circuits 4 & 5
Calculate the current for both circuits. What is the difference between the circuits?
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 amp?
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?
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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.
What is a short circuit?
A short circuit occurs when there is (at least) one path in a circuit with zero (or near-zero) resistance.
Since there is no resistance, the current flow approaches:
Short circuits are not valid either.
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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Review Questions
30. In an experiment that measures how fast a student reacts, a meter stick dropped from rest falls 0.20
meter before the student catches it. What is the reaction time of the student?
31. A 40-kilogram student runs up a staircase to a floor that is 5.0 meters higher than her starting point
in 7.0 seconds. The student’s power output is
32. Which pair of concurrent forces could produce a resultant force having a magnitude of 10N?
1)
10 N, 10 N
3)
4.7 N, 4.7 N
2)
10 N, 30 N
4)
4.7 N, 5 N
Electrical Power
Electric Potential Difference – 1 Volt =
As electrons travel through circuits, they do work.
How much potential energy does each Coulomb of charge have in a 1V battery?
How much work can each Coulomb of charge do in a 1V battery?
Recall,
Power =
Power in Circuits depends on:
How much energy each unit of charge has -> ____________
More ____________ means more energy per Coulomb -> ____________ power
How many electrons are flowing through it -> ____________
More ____________ means more charge means ->____________ power
Power =
Watt is the unit for power?
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How does a light bulb work?
Believe it or not, Thomas Edison did not invent the light bulb.
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.
Problems
33. What is the power generated in a circuit that conducts 10A of current when connected to a 15V
battery?
34. How much current is drawn by a 800W light bulb when it is connected to a 20V power supply?
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?
36. How much work is done by an 80 W light bulb in 2 minutes?
37. How much power is used by a 20 Ohm resistor connected to a 10V voltage source? Draw a diagram
38. How much current is flowing through a 100W circuit with a 10 Ohm resistor?
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Review Questions
39. An object initially traveling in a straight line with a speed of 5.0 meters per second is accelerated at
2.0 meters per second2 for 4 seconds. The total distance traveled by the object in the 4 seconds is:
40. What force is needed to give an electron an acceleration of 1 x 1010 meters per second?
41. A 1750 kg car travels at a constant speed of 5 m/s around a horizontal circular track with a radius of
45 m. What is the magnitude of the centripetal force acting on the car?
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
Identify whether the following are in series or parallel
Are the 2 resistors in series or parallel?
Are the 2 resistors in series or parallel?
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Are the two resistors in series or parallel?
Is the 20 Ohm resistor in series or parallel with the Voltmeter (V)?
Are the two resistors in series or parallel?
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?
A
B
C
D
Now assume each is a wire is made of copper. Which will have the most resistance? Which will have
the least? Why?
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?
A
B
C
D
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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.
=
Find the equivalent resistance of this circuit. Then find the current of the 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.
What is the potential difference for the entire circuit? Does this match up with the battery?
For any series circuit:
I=
V=
Req =
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.
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Parallel Circuit
Resistors in parallel is like increasing the cross-sectional 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.
Find the equivalent resistance of this circuit. Then find the current of the circuit.
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.
For any parallel circuit:
I=
V=
Req =
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.
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Review Questions
42. A race car traveling at 10 meters per second accelerates at a rate of 1.5 meters per second2 while
traveling a distance of 600 meters. What is the final speed of the race car?
43. A horizontal force is used to pull a 5.0 kilogram cart at a constant speed of 5.0 meters per second
across the floor, as shown in the diagram. If the force of friction between the cart and the floor is 10
newtons, what is the magnitude of the horizontal force along the handle of the cart?
44. How much work is done on a downhill skier by an average braking force of 9.8 x 102 newtons to
stop her in a distance of 10 meters?
Measuring Current
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?
Series
Parallel
Similarly, ammeters are always connected in series.
Ammeters have very low internal resistance, to not interfere with the circuit being measured.
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45. Finish the following drawing: The battery is connected to a 5 Ohm resistor and an ammeter is set
up to measure current.
What will the ammeter read?
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.
What will the ammeter read?
In a parallel circuit, an ammeter can tell you the current for each individual path on the circuit.
Ammeter 2 is set up to measure current through the
path with the 20 Ohm resistor.
Ammeter 3 is set up to measure current through the
path with the 30 Ohm resistor.
If the current through A1 is 10 Amps, and the current through A2 is 6 Amps, what is the current through
A3?
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
47. Draw a voltmeter connected to the 3 Ohm resistor. What will it read?
Resistance:
Current:
Voltage:
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48. Draw a voltmeter connected to the 4 Ohm resistor. What will it read?
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?
51.
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?
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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
Calculate the equivalent resistance of the circuit
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.
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Junction Rule
The total current (traffic) into a junction is equal to the total current (traffic) out of the junction
Review Checklist
Explain how electrical potential relates to changes in distance between charged objects. Use equation to
determine electrical potential, work/energy, and/or charge. Convert between joules and electron-volts.
1. What is the electrical potential generated when 15.0 joules of work are done in moving a 5.0 coulomb
charge through an electric field?
2. What is the amount of work needed to increase the electrical potential of a 2.0 coulomb charge by 8.0
volts?
3. What is the amount of energy needed to move an electron through an electrical potential of 3.0 volts?
Express this energy in both joules and electron-volts.
4. An object with a 4.0 coulomb charge is accelerated through an electrical potential of 12.0 volts. What
amount of kinetic energy does the object gain? Express this energy in both joules and electron-volts.
Use electrical current equation to determine current, charge, or time. Determine number of electrons
flowing based on current or current based on number of electrons.
5. What is the amount of electrical current passing through a wire if 35 coulombs of charge flow
through it in 5.0 seconds?
6. If a 2.5 ampere current is flowing through a given point on a wire, how long would it take for 100
coulombs of charge to pass this point?
7. How much charge passes through a wire if a current of 10 ampere flows through it for 30 seconds?
8. How many electrons per second are flowing through a point in a wire that has 5.0 amperes of current
passing through it?
9. 6.4 x 1014 electrons pass through a given point every second. What amount of electrical current does
this represent?
20
Use equation to determine resistance, resistivity, length and/or cross-sectional area. Determine
composition of a wire. Explain the relationship between resistance and various factors that impact
resistance.
10. What is the resistance of a copper wire with a cross-sectional area of 2.0 x 10-6 meter2 and a length
of 50 meters?
11. What is the length of an aluminum wire with a resistance of 25 milliohms if it has a cross-sectional
area of 4.0 x 10-4 meter2 ?
12. What is the composition of a wire with a resistance of 8.13 ohms if its crosssectional area is 3 x 10-6
meter2 and its length is 1000 meters?
13. Compared to wire A which has a resistance of 10 ohms, wire B has twice the length and half the
cross-sectional area. What is the resistance of wire B?
Use Ohm’s Law and Power Law to perform calculations. Analyze graphs to relate voltage, current,
resistance, and/or power. Recognize and sketch simple circuits with switches, batteries, meters, and/or
resistances.
14. How much current will pass through a 30 ohm resistor when it is connected to a 90 volt source of
electrical potential?
15. What is the resistance of a heater that allows 12 amperes of current to flow through it when it is
connected to a 120 volt source?
16. How much power is generated by a light bulb that draws 0.2 ampere of current when connected to a
6.0 volt battery?
17. How much current is drawn by a 4400 watt motor if it is operated at an electrical potential of 220
volts?
18. What is the resistance of a component that generates 300 watts of power while allowing 0.5 ampere
of current to pass through it?
Explain the difference between series and parallel circuits. Explain how the Junction Rule works and
use it to determine unknown currents. Solve circuits of either type using charts, Ohm’s Law, and Power
Law. Determine the effect of adding/removing resistors and opening/closing switches on circuits.
Compare equivalent resistances of different circuits and/or arrangements of resistors.
19. A 30 ohm resistor and a 20 ohm resistor are connected in series with a 100 volt battery. The
electrical current that would pass through the 20 ohm resistor is
20. A 30 ohm resistor and a 20 ohm resistor are connected in parallel with a 100 volt battery. The
electrical current that would pass through the 20 ohm resistor is
21. A 30 ohm resistor and a 20 ohm resistor are connected in series with a 100 volt battery. The
electrical potential that is measured across the 30 ohm resistor in this circuit would be:
22. A 30 ohm resistor and a 20 ohm resistor are connected in parallel with a 100 volt battery. The
electrical potential that is measured across the 30 ohm resistor in this circuit would be:
21
23. Determine the equivalent resistance of…
a. three 90 ohm resistors in series
b. three 90 ohm resistors in parallel
c. a 10 ohm resistor and 20 ohm resistor in series
d. a 10 ohm resistor and 20 ohm resistor in parallel
e. 5, 10, and 40 ohm resistors in series
f. 20, 30, and 40 ohm resistors in parallel
g. 120, 142, and 312 ohm resistors in series
h. 311, 416, and 520 ohm resistors in parallel
24. Determine the unknown current and its direction in each diagram.
25. Two 20 ohm resistors are connected in parallel. If a third 20 ohm resistor is connected to them in
parallel the equivalent resistance of the circuit will
(1) increase (2) decrease (3) not change
26. Two 20 ohm resistors are connected in series. If a third 20 ohm resistor is connected to them in
series the equivalent resistance of the circuit will
(1) increase (2) decrease (3) not change
Answers
d. 6.67 Ω
1. 3 V
e. 55 Ω
2. 16 J
f. 9.2 Ω
3. 3eV, 4.8 x 10-19 J
g. 574 Ω
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4. 48 J, 3 x 10 eV
h. 133 Ω
5. 7 A
24. 2 A right
6. 40 s
4 A left
7. 300 C
2 A left
8. 3.13 x 1019
25. 2
9. 0.0001A
26. 1
10. 0.43 Ω
11. 354.6 m
12. Gold
13. 40 Ω
14. 3 A
15. 10 Ω
16. 1.2 W
17. 20 A
18. 1200 Ω
19. 2 A
20. 5 A
21. 60 V
22. 100 V
23. A. 270 Ω
b. 30 Ω
c. 30 Ω
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