Name: 
 

Electrical Energy and Capacitance


Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
 

1. 
Which of the following is NOT a characteristic of electrical potential energy?
a.
It is a form of mechanical energy.
b.
It results from a single charge.
c.
It results from the interaction between charges.
d.
It is associated with a charge in an electric field.
 

2. 
When a positive charge moves because of a force, what happens to the electrical potential energy associated with the charge’s position in the system?
a.
It increases.
c.
It remains the same.
b.
It decreases.
d.
It sharply increases, and then decreases.
 

3. 
Two positive point charges are initially separated by a distance of 2 cm. If their separation is increased to 6 cm, the resultant electrical potential energy is equal to what factor times the initial electrical potential energy?
a.
3
c.
electric_forces_and_files/i0040000.jpg
b.
9
d.
electric_forces_and_files/i0040001.jpg
 

4. 
A proton (q = 1.60 ´ 1019 C) moves 10.0 cm on a path parallel to the direction of a uniform electric field of strength 3.0 N/C. What is the change in electrical potential energy?
a.
4.8 ´ 10–20 J
c.
–4.8 ´ 10–20 J
b.
1.6 ´ 10–20 J
d.
–1.6 ´ l0–20 J
 

5. 
A uniform electric field with a magnitude of 5.0 ´ 102 N/C is directed parallel to the positive x-axis toward the origin. What is the change in electrical energy of a proton (q = 1.60 ´ 10–19 C) as it moves from x = 5 m to x = 2 m?
a.
8.0 ´ 10–17 J
c.
2.0 ´ 1021 J
b.
2.0 ´ 10–16 J
d.
500 J
 

6. 
Two point charges with values of 3.4 mC and 6.6 C are separated by 0.20 m. What is the electrical potential energy of this two-charge system?
a.
0.34 J
c.
1.0 J
b.
–0.75 J
d.
–3.4 J
 

7. 
Two protons, each having a charge of 1.60 ´ 10–19 C, are 2.0 ´ 10–5 m apart. What is the electrical potential energy between the two charges?
a.
1.1 ´ 10–23 J
c.
3.2 ´ 10–16 J
b.
3.2 ´ 10–19 J
d.
1.6 ´ 10–14 J
 

8. 
When an electron (e = –1.6 ´ 10–19 C) moves 0.10 m along the direction of an electric field with a strength of 3.0 N/C, what is the magnitude of the potential difference between the electron’s initial and final points?
a.
4.8 ´ 10–19 V
c.
0.03 V
b.
0.30 V
d.
3.0 ´ 101 V
 

9. 
Four point charges are positioned on the circumference of a circle with a radius of 10 cm. The charges are 0.5 mC, 1.5 mC, –1.0 mC, and –0.5 mC, respectively. If the electric potential at the center of the circle 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? (Hint: Use the superposition principle.)
a.
1.80 ´ 104 V
c.
0.0 V
b.
4.5 ´ 104V
d.
–4.5 ´ 104 V
 

10. 
A uniform electric field with a magnitude of 500 N/C is directed parallel to the positive x-axis. If the potential at x = 5 m is 2500 V, what is the potential at x = 2 m?
a.
1000 V
c.
4000 V
b.
2000 V
d.
4500 V
 

11. 
What will be the electric potential at a distance of 0.15 m from a point charge of 6.0 mC?
(kc = 8.99 ´ 109 N·m2/C2)
a.
5.4 ´ 104 V
c.
2.4 ´ 106 V
b.
3.6 ´ 106 V
d.
1.2 ´ 107 V
 

12. 
Two point charges with values of 3.4 mC and 6.6 mC are separated by 0.10 m. What is the electric potential at the point midway between the two point charges? (kc = 8.99 ´ 109 N·m2/C2)
a.
1.8 ´ 106 V
c.
0.9 ´ 106 V
b.
–0.9 ´ 106 V
d.
3.6 ´ 106 V
 

13. 
At what distance from a point charge of 8.0 mC would the electric potential be 4.2 ´ 104 V?
(kc = 8.99 ´ 109 N·m2/C2)
a.
0.58 m
c.
1.7 m
b.
0.76 m
d.
2.9 m
 

14. 
A point charge of 3.0 mC is at the origin of a coordinate system, and a second point charge of –6.0 mC is at x = 1.0 m. What is the electric potential at the point where x = 0.50 m? (kc = 8.99 ´ 109 N·m2/C2)
a.
1.62 ´ 105 V
c.
–1.08 ´ 105 V
b.
1.08 ´ 105V
d.
–5.4 ´ 104 V
 

15. 
Charge build up between the plates of a capacitor stops when
a.
there is no net charge on the plates.
b.
unequal amounts of charge accumulate on the plate.
c.
the potential difference between the plates is equal to the potential difference between the terminals of the battery.
d.
the charge on both plates is the same.
 

16. 
When comparing the net charge of a charged capacitor with the net charge of the same capacitor when it is uncharged, the net charge is
a.
greater in the charged capacitor.
b.
less in the charged capacitor.
c.
equal in both capacitors.
d.
greater or less in the charged capacitor, but never equal.
 

17. 
When a capacitor discharges,
a.
it must be attached to a battery.
b.
charges move back from one plate to another through the circuit until both plates are uncharged.
c.
charges move from one plate to another until equal and opposite charges accumulate on the plates.
d.
it cannot be connected to a material that conducts.
 

18. 
A capacitor consists of two metal plates; ____ is stored on one plate and ____ is stored on the other.
a.
negative charge; positive charge
c.
potential difference; internal resistance
b.
potential energy; kinetic energy
d.
residual charge; induced charge
 

19. 
Increasing the separation of the two charged parallel plates of a capacitor when they are disconnected from a battery will produce what effect on the capacitor?
a.
It will increase the charge.
c.
It will increase the capacitance.
b.
It will decrease the charge.
d.
It will decrease the capacitance.
 

20. 
Increasing the potential difference across the two plates of a capacitor will produce what effect on the capacitor?
a.
It will increase the charge.
c.
It will increase the capacitance.
b.
It will decrease the charge.
d.
It will decrease the capacitance.
 

21. 
A 0.25 mF capacitor is connected to a 9.0 V battery. What is the charge on the capacitor?
a.
1.2 ´ 10–12 C
c.
2.8 ´ 10–8 C
b.
2.2 ´ 10–6 C
d.
3.6 ´ 10–7 C
 

22. 
A parallel-plate capacitor has a capacitance of C F. If the area of the plates is doubled while the distance between the plates is halved, the new capacitance will be
a.
2 C.
c.
electric_forces_and_files/i0230000.jpg.
b.
4 C.
d.
electric_forces_and_files/i0230001.jpg.
 

23. 
What is the capacitance of a parallel-plate capacitor made of two square aluminum plates that are 4.0 cm in length on each side and are separated by 5.0 mm? (e0 = 8.85 ´ 10–12 C2/N·m2)
a.
2.8 ´ 10–10 F
c.
2.8 ´ 10–12 F
b.
1.0 ´ 10–6 F
d.
2.0 ´ 10–5 F
 

24. 
A 0.50 mF capacitor is connected to a 12 V battery. How much electrical potential energy is stored in the capacitor?
a.
2.0 ´ 10–12 J
c.
0.04 J
b.
1.0 ´ 10–12 J
d.
3.6 ´ 10–5 J
 

25. 
A 1.5 mF capacitor is connected to a 9.0 V battery. How much energy is stored in the capacitor?
a.
1.7 ´ 10–3 J
c.
7.5 ´ 10–3 J
b.
6.1 ´ 10–5 J
d.
5.4 ´ 10–3 j
 

Short Answer
 

26. 
What is electrical potential energy?
 

27. 
Electrical potential energy is a result of what interaction?
 

28. 
What is electric potential?
 

29. 
What is potential difference?
 

30. 
How are electric potential and electrical potential energy related?
 

31. 
What is capacitance?
 

32. 
How does a capacitor store energy?
 

33. 
Explain why there is a limit to the amount of charge that can be stored on a capacitor.
 

34. 
List two ways to increase the electrical potential energy that can be stored in a capacitor.
 

Problem
 

35. 
A proton (q = 1.60 ´ 10–19 C) moves 16.0 cm on a path parallel to the direction of a uniform electric field of strength 3.0 N/C. What is the change in electrical potential energy?
 

36. 
A proton (q = 1.60 ´ 10–19 C) moves 26 cm on a path parallel to the direction of a uniform electric field of strength 4.0 N/C. What is the change in electrical potential energy?
 

37. 
A proton (q = 1.60 ´ 10–19 C) moves 38 cm on a path parallel to the direction of a uniform electric field of strength 1.5 N/C. What is the change in electrical potential energy?
 

38. 
A proton (q = 1.60 ´ 10–19 C) moves 12 cm on a path parallel to the direction of a uniform electric field of strength 6.0 N/C. What is the change in electrical potential energy?
 

39. 
A proton (q = 1.60 ´ 10–19 C) moves 24 cm on a path parallel to the direction of a uniform electric field of strength 5.0 N/C. What is the change in electrical potential energy?
 

40. 
A proton (q = 1.60 ´ 10–19 C) moves 96 cm on a path parallel to the direction of a uniform electric field of strength 1.0 N/C. What is the change in electrical potential energy?
 

41. 
A proton (q = 1.60 ´ 10–19 C) moves 47 cm on a path parallel to the direction of a uniform electric field of strength 3.6 N/C. What is the change in electrical potential energy?
 

42. 
A proton (q = 1.60 ´ 10–19 C) moves 73 cm on a path parallel to the direction of a uniform electric field of strength 2.2 N/C. What is the change in electrical potential energy?
 

43. 
A proton (q = 1.60 ´ 10–19 C) moves 68 cm on a path parallel to the direction of a uniform electric field of strength 2.8 N/C. What is the change in electrical potential energy?
 

44. 
A 3.2 mF capacitor has a potential difference of 21.0 V between its plates. How much additional charge flows into the capacitor if the potential difference is increased to 47.0 V?
 

45. 
A 0.63 mF capacitor is connected to a 3.0 V battery. How much energy is stored in the capacitor?
 

46. 
A 3.2 mF capacitor is connected to a 1.5 V battery. How much energy is stored in the capacitor?
 

47. 
A 6.0 mF capacitor holds 3.0 mC of charge. How much potential energy is stored in the capacitor?
 

48. 
A 0.75 mF capacitor holds 6.0 mC of charge. How much potential energy is stored in the capacitor?
 

49. 
A 0.10 mF capacitor holds 9.0 mC of charge. How much potential energy is stored in the capacitor?
 

50. 
A 0.42 mF capacitor holds 1.0 mC of charge. How much potential energy is stored in the capacitor?
 

51. 
A 0.5 F capacitor is connected to a 1.5 V battery. How much energy is stored in the capacitor?
 

52. 
A 0.10 F capacitor is connected to a 4.0 V battery. How much energy is stored in the capacitor?
 



 
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