Electrical Energy and Capacitance
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1. A 9.0-V battery is connected between two parallel metal plates 4.0 mm apart. What is the magnitude of the
electric field between the plates?
c. 2.3 N/C
a. 2.3  103 N/C
b. 9.0 N/C
d. 0.75  106 N/C
____
2. A free electron is in an electric field. With respect to the field, it experiences a force acting:
a. parallel.
c. perpendicular.
b. anti-parallel (opposite in direction).
d. along a constant potential line.
____
3. If the distance between two negative point charges is increased by a factor of three, the resultant potential
energy is what factor times the initial potential energy?
a. 3.0
c. 1/3
b. 9.0
d. 1/9
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4. An electron in a TV picture tube is accelerated through a potential difference of 10 kV before it hits the
screen. What is the kinetic energy of the electron in electron volts? (1 eV = 1.6  1019 J)
a. 1.0  104 eV
c. 1.6  1022 eV
15
b. 1.6  10 eV
d. 6.25  1022 eV
____
5. Electrons in an x-ray machine are accelerated from rest through a potential difference of 50 000 V. What is
the kinetic energy of each of these electrons in eV?
a. 50 eV
c. 330 eV
b. 80 eV
d. 50 keV
____
6. A 0.25-F capacitor is connected to a 400-V battery. Find the charge on the capacitor.
a. 1.2  1012 C
c. 0.040 C
4
b. 1.0  10 C
d. 0.020 C
____
7. A 20-F capacitor is attached across a 1000-V power supply. What is the net charge on the capacitor?
a. 10 mC
c. 40 mC
b. 20 mC
d. none of the above
____
8. If three 4.0-µF capacitors are connected in parallel, what is the combined capacitance?
c. 8.0 F
a. 12 F
d. 0.46 F
b. 0.75 F
____
9. An electron (charge 1.6  1019 C) moves on a path perpendicular to the direction of a uniform electric field
of strength 3.0 N/C. How much work is done on the electron as it moves 15 cm?
a. 4.8  1020 J
c. 1.6  1020 J
20
b. 4.8  10 J
d. zero
____ 10. A proton (+1.6  1019 C) moves 10 cm on a path in the direction of a uniform electric field of strength 3.0
N/C. How much work is done on the proton by the electrical field?
c. 1.6  1020 J
a. 4.8  1020 J
b. 4.8  1020 J
d. zero
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____ 11. A proton (+1.6  1019 C) moves 10 cm along the direction of an electric field of strength 3.0 N/C. The
electrical potential difference between the proton’s initial and ending points is:
a. 4.8  1019 V.
c. 0.033 V.
b. 0.30 V.
d. 30 V.
____ 12. If an electron is accelerated from rest through a potential difference of 1 200 V, find its approximate velocity
at the end of this process. (e = 1.6  1019 C; me = 9.1  1031 kg)
a. 1.0  107 m/s
c. 2.1  107 m/s
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b. 1.4  10 m/s
d. 2.5  107 m/s
____ 13. A uniform electric field, with a magnitude of 600 N/C, is directed parallel to the positive x-axis. If the
potential at x = 3.0 m is 1 000 V, what is the potential at x = 1.0 m?
a. 400 V
c. 2 200 V
b. 1 600 V
d. 2 500 V
____ 14. A uniform electric field, with a magnitude of 600 N/C, is directed parallel to the positive x-axis. If the
potential at x = 3.0 m is 1 000 V, what is the change in potential energy of a proton as it moves from x = 3.0 m
to x = 1.0 m? (qp = 1.6  1019 C)
a. 8.0  1017 J
c. 0.80  1021 J
16
b. 1.9  10 J
d. 500 J
____ 15. An electron in a cathode ray tube is accelerated through a potential difference of 5.0 kV. What kinetic energy
does the electron gain in the process? (e = 1.6  1019 C)
a. 1.6  1016 J
c. 1.6  1022 J
b. 8.0  1016 J
d. 8.0  1022 J
____ 16. An electron is released from rest at the negative plate of a parallel-plate capacitor. If the distance across the
plate is 5.0 mm and the potential difference across the plate is 5.0 V, with what velocity does the electron hit
the positive plate? (me = 9.1  1031 kg, e = 1.6  1019 C)
a. 2.6  105 m/s
c. 1.0  106 m/s
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b. 5.3  10 m/s
d. 1.3  106 m/s
____ 17. A 9.0-V battery moves 20 mC of charge through a circuit running from its positive terminal to its negative
terminal. How much energy was delivered to the circuit?
a. 2.2 mJ
c. 0.18 J
b. 0.020 J
d. 4.5  103 J
____ 18. Four point charges are on the rim of a circle of radius 10 cm. The charges are (in C) +0.50, +1.5, 1.0,
0.50. If the electrical potential at the circle’s center due to the +0.5 charge alone is 4.5  104 V, what is the
total potential at the center due to the four charges combined?
a. 18  104 V
c. zero
b. 4.5  104 V
d. 4.5  104 V
____ 19. Find the electrical potential at 0.15 m from a point charge of 6.0 C. (ke = 8.99  109 Nm2/C2)
a. 5.4  104 V
c. 2.4  106 V
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b. 3.6  10 V
d. 1.2  107 V
2
____ 20. Two point charges of values +3.4 and +6.6 C, respectively, are separated by 0.20 m. What is the potential
energy of this 2-charge system? (ke = 8.99  109 Nm2/C2)
a. +0.34 J
c. +1.0 J
b. 0.75 J
d. 3.4 J
____ 21. Two point charges of values +3.4 and +6.6 C are separated by 0.10 m. What is the electrical potential at the
point midway between the two point charges? (ke = 8.99  109 Nm2/C2)
a. +1.8  106 V
c. +0.90  106 V
b. 0.90  106 V
d. +3.6  106 V
____ 22. At what distance from a point charge of 8.0 C would the electrical potential be 4.2  104 V? (ke = 8.99  109
Nm2/C2)
a. 0.58 m
c. 1.7 m
b. 0.76 m
d. 2.9 m
____ 23. A point charge of +3.0 C is located at the origin of a coordinate system and a second point charge of 6.0
C is at x = 1.00 m. What is the electric potential at the x = 0.50 m point? (ke = 8.99  109 Nm2/C2)
a. 16  104 V
c. 11  104 V
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b. 11  10 V
d. 5.4  104 V
____ 24. A point charge of +3.0 C is located at the origin of a coordinate system and a second point charge of 6.0
C is at x = 1.0 m. At what point on the x axis is the electrical potential zero?
a. 0.25 m
c. +0.33 m
b. +0.25 m
d. +0.75 m
____ 25. Two protons, each of charge 1.60  10-19 C, are 2.00  10-5 m apart. What is the change in potential energy if
they are brought 1.00  10-5 m closer together? (ke = 8.99  109 N·m2/C2)
a. 1.15  1023 J
c. 3.20  1016 J
19
b. 3.20  10 J
d. 1.60  1014 J
____ 26. When charge Q1 is placed at point P1, the resulting potential at point P is V 1. When Q2 is placed at point P2
after Q1 is in position at P1, the resulting potential at P becomes V2. What is the potential at point P if charge
Q1 is then removed?
c. V2 – V1
a. V1 + V2
b. V1 – V2
d. (V1 + V2)/2
____ 27. If a doubly-ionized oxygen atom (O –2) is accelerated from rest by going through a potential difference of 20
V, what will be the change in its kinetic energy?
a. 10 eV
c. 40 eV
b. 20 eV
d. none of the above
3
____ 28. There is a hollow, conducting, uncharged sphere with a negative charge inside the sphere. Consider the
electrical potential at the inner and outer surfaces of the sphere. Which of the following is true?
a.
b.
The potential on the inner surface is
greater.
The potential on the outer surface is
greater.
c.
The potentials on both surfaces are zero.
d.
The potentials on both surfaces are equal
but not zero.
____ 29. A parallel-plate capacitor has a capacitance of 20 µF. What potential difference across the plates is required to
store 7.2  104 C on this capacitor?
a. 36 V
c. 1.4  108 V
b. 2.2  10-2 V
d. 68 V
____ 30. Three capacitors of 1.0, 1.5, and 2.0 F are connected in series. Find the combined capacitance.
a. 4.5 F
c. 2.2 F
b. 4.0 F
d. 0.46 F
____ 31. Two capacitors with capacitances of 1.5 and 0.25 F, respectively, are connected in parallel. The system is
connected to a 50-V battery. What charge accumulates on the 1.5- F capacitor?
a. 100 C
c. 50 C
b. 75 C
d. 33 C
____ 32. Two capacitors with capacitances of 1.0 and 0.50 F, respectively, are connected in series. The system is
connected to a 100-V battery. What charge accumulates on the 1.0- F capacitor?
a. 150 C
c. 50 C
b. 100 C
d. 33 C
____ 33. Two capacitors with CA greater than CB and are connected in series with a battery. Which of the following is
true?
a. There is more charge stored on CA.
c. There is the same charge stored on each
capacitor.
b. There is more charge stored on CB.
d. There is the same potential difference
across both capacitors.
____ 34. Two capacitors with CA greater than CB are connected in parallel with a battery. Which of the following is
true?
a. There is more potential difference across c. There is the same charge stored on each
capacitor.
CA.
b. There is more potential difference across d. There is the same potential difference
across both capacitors.
CB.
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____ 35. What is the equivalent capacitance between points a and b? All capacitors are 1.0 F.
a.
b.
4.0 µF
1 7 µF
c.
d.
0.60 µF
0.25 µF
____ 36. If C = 36 µF, determine the equivalent capacitance for the combination shown.
a.
b.
36 µF
32 µF
c.
d.
28 µF
24 µF
____ 37. If C = 10 µF, what is the equivalent capacitance for the combination shown?
a.
b.
7.5 µF
6.5 µF
c.
d.
7.0 µF
5.8 µF
____ 38. What is the equivalent capacitance of the combination shown?
a.
b.
29 µF
10 µF
c.
d.
40 µF
25 µF
____ 39. What is the equivalent capacitance of the combination shown?
a.
b.
24 µF
100 µF
c.
d.
5
12 µF
4.6 µF
____ 40. Four identical 1 mF capacitors are connected together electrically. What is the least possible capacitance of
the combination?
a. 4 mF
c. 1/4 mF
b. 1 mF
d. 1/8 mF
____ 41. Four identical 1-mF capacitors are connected together electrically. What is the greatest possible capacitance
of the combination?
a. 8 mF
c. 1 mF
b. 4 mF
d. 1/4 mF
____ 42. A 10.0-F capacitor is attached to a 20-V power supply. How much energy is stored in the capacitor?
a. 2.0  103 J
c. 2.0  104 J
3
b. 1.2  10 J
d. 5.2  104 J
____ 43. A 0.25-F capacitor is connected to a 400-V battery. What potential energy is stored in the capacitor?
a. 1.2  1012 J
c. 0.040 J
4
b. 1.0  10 J
d. 0.020 J
____ 44. Two capacitors with capacitances of 1.5 F and 0.25 F, respectively, are connected in parallel. The system is
connected to a 50-V battery. What electrical potential energy is stored in the 1.5- F capacitor?
a. 0.50  103 J
c. 1.9  103 J
b. 1.2  103 J
d. 10.0  103 J
____ 45. A “sandwich” is constructed of two flat pieces of metal (2.00 cm on a side) with a 2.00-mm-thick piece of a
dielectric called Rutile ( = 100) in between them. What is the capacitance? ( 0 = 8.85  1012 C2/Nm2)
a. 177 pF
c. 8.85 µF
b. 885 nF
d. 100 µF
____ 46. Very large capacitors have been considered as a means for storing electrical energy. If we constructed a very
large parallel-plate capacitor of plate area 1.0 m2 using paper ( = 3.7) of thickness 1.0 mm as a dielectric,
how much electrical energy would it store at a plate voltage of 5 000 V? ( 0 = 8.85  1012 C2/Nm2)
a. 0.41 J
c. 9 000 J
b. 90 J
d. 45 000 J
____ 47. A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to double the original
separation, the charges on the plates remaining the same. What is the ratio of the final energy stored to the
original energy stored?
a. 4
c. 1
b. 2
d. 1/2
____ 48. A pair of parallel plates, forming a capacitor, are connected to a battery. While the capacitor is still connected
to the battery maintaining a constant voltage, the plates are pulled apart to double their original distance.
What is the ratio of the final energy stored to the original energy stored?
a. 2
c. 1/2
b. 1
d. 1/4
____ 49. Two parallel-plate capacitors have the same plate area, and the gap between the plates is filled with a
dielectric with a dielectric constant equal to 4. The gap in capacitor A is one half that in Capacitor B. What
is the ratio of the capacitance of A to B?
a. 2
c. 1/2
b. 1
d. The ratio is not given.
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____ 50. A capacitor is made by taking two sheets of aluminum foil, each 0.022 mm thick and placing between them a
sheet of paper which comes from a ream of 500 sheets, the ream being 5.5 cm thick with sheets measuring
216 mm by 279 mm (the usual 8 1/2 by 11). What is the capacitance of the capacitor made this way if the
dielectric constant of the paper is 3.7? ( 0 = 8.85  10-12 C2/N  m2)
a. 24 nF
c. 18 nF
b. 48 nF
d. 1.3 nF
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ID: A
Electrical Energy and Capacitance
Answer Section
MULTIPLE CHOICE
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ID: A
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