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PHYS102 Previous Exam Problems –
CHAPTER
25
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Capacitance
Calculating the capacitance
Combination of capacitors
Energy stored in capacitors
Capacitors with dielectrics
1. Given a 9.4-pF air-filled capacitor, you are asked to convert it to a capacitor that can store 9.4 μJ, with a
potential of 877 V. What is the dielectric constant of the material that you must insert between the plates of the
capacitor? (Ans: 2.6)
2. A capacitor C 1 = 1.00 µF and another capacitor C 2 = 2.00 µF are connected in series across a 900-V supply
line. The charged capacitors are disconnected from the supply line then reconnected to each other with terminals
of like sign together. Find the final charges on C 1 and C 2 , respectively. (Ans: 400 µC, 800 µC)
3. Two capacitors each of capacitance 250 µF are connected in parallel across a battery of 120 V. How
much energy is produced after both capacitors are completely discharged? (Ans: 3.6 J)
4. The magnitude of the charge on each plate of a parallel plate capacitor is 2.5 μC. If the capacitor has a plate
area of 0.25 m2 and a plate separation of 0.1 mm, what is the electric field between its plates?
(Ans: 1.1×106 V/m)
5. Figure 1 shows two capacitors C 1 = 30 μF carrying a charge q 1 = 200 μC, and C 2 = 20 μF carrying a charge
q 2 = 900 μC. If the switches S are closed, what is the voltage across C 1 ? (Ans: 14 V)
6. If C = 12 μF and the potential difference between points A and B is 10 V, what is the total energy stored
by the group of capacitors shown in figure 2? (Ans: 300 μJ)
7. An air-filled parallel-plate capacitor is connected across a 24-V battery. When the battery is disconnected
and then a dielectric slab is inserted into and fills the region between the plates, the voltage across the capacitor
drops to 8 V. What is the dielectric constant of the slab? (Ans: 3.0)
8. The three capacitors in the figure 3 have an equivalent capacitance of 2.77 μF. What is C 2 ? (Ans: 7 μF)
9. When the potential difference across a 5-μF capacitor is increased by 2 V, the energy stored increases by 10
%. What was the original potential difference? (Ans: 41 V)
10. In figure 4: C 1 = 4.0 µF, C 2 = 12 µF, C 3 = 2.0 µF, and V = 9.0 V. What is the charge on capacitor C 3 ?
(Ans: 16 μC)
11. A parallel-plate capacitor is completely filled with a dielectric of dielectric constant 6, and has a
capacitance of 50 pF. If the plate separation is 0.1 mm, find the plate area. (Ans: 0.94 cm2)
12. How much energy is stored in the combination of capacitors shown figure 5? (Ans: 0.03 J)
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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13. Figure 7 shows three capacitors connected to a battery of voltage V = 6 V. The charges on the capacitors
are known to be Q 1 = 24 µC for C 1 and Q 2 = 96 µC for C 2 . What are the values of the capacitances C 1 and C 2 ?
(Ans: C 1 =8 µF, C 2 = 16 µF)
14. A parallel-plate capacitor has square-shaped plates with an area of 4.1×10-3 m2, and 1.6×10-3 m separation.
What charge will appear on the plates of such a capacitor if a potential difference of 80 V is applied?
(Ans: 1.8×10-9 C)
15. An air-filled parallel-plate capacitor has a capacitance of 3.0×10−12 F. The plate separation is then doubled
and a wax dielectric is inserted, completely filling the space between the plates. As a result, the capacitance
becomes 7.5×10−12 F. What is the dielectric constant of the wax? (Ans: 5.0)
16. A battery having potential difference V = 12 V and four capacitors, each having a capacitance of 12 µF,
are connected as shown in the figure 8. What is the charge on C 2 ? (Ans: 72 µC)
17. Consider the combination of capacitors shown in figure 9. The energy stored in the 8.0-µF capacitor is
0.40 J. What is the energy stored in the 5.0-µF capacitor? (Ans: 0.25 J)
18. Each of the four capacitors shown in figure 10 is 500 μF. The voltmeter reads 1000 V. What is the
magnitude of the charge, on each capacitor plate? (Ans: 0.5 C)
19. A parallel-plate capacitor has a plate area of 0.20 m2 and a plate separation of 0.10 mm. The electric field
between the plates is 2.0 × 106 V/m. How much energy is stored in the capacitor? (Ans: 0.35 mJ)
20. Capacitors A and B have the same capacitance. Capacitor A is charged so that it stores 4 J of energy and
capacitor B is uncharged. The capacitors are then connected in parallel. What will be the total stored energy
after the combination? (Ans: 2 J)
21. Consider the arrangement of capacitors shown in figure 11. Find the energy stored in the 5-µF
capacitor. (Ans: 0.56 mJ)
22. A dielectric material is inserted completely between the plates of a capacitor. If the potential difference is
kept constant, and the charge was increased by 60%, determine the dielectric constant of the material. (Ans: 1.6)
23. Two capacitors, C 1 = 2 µF and C 2 = 6 µF, are connected in parallel to a 60-V battery, as shown in figure
12. The battery is removed and plates of opposite sign are connected. Find the final potential difference for each
capacitor. (Ans: 30 V, 30 V)
24. A 25-µF parallel-plate capacitor is constructed using Pyrex glass as a dielectric. If the thickness of the
Pyrex glass sheet is doubled, calculate the new capacitance of the capacitor. [dielectric constant of Pyrex glass =
5.6] (Ans: 12.5 µF)
25. In figure 13, V o = 4.4 V, how much energy is stored in the 50-µF capacitor? (Ans: 0.48 mJ)
26. Three capacitors C 1 = 5 µF, C 2 = 10 µF, and C 3 = 3 µF are connected to a 20-V battery as shown in
figure 14. Find the stored electric energy in C 2 . (Ans: 2.2×10-4 J)
27. A parallel-plate capacitor (with plates A and B) has circular shape of radius 6.0 cm separated by 2.0 mm.
Find the total charges on both plates (A and B) when a 12 V battery is connected. (Ans: zero)
28. The three capacitors in figure 15 have an equivalent capacitance of 12.4 µF, find the capacitance of C 1 .
(Ans: 6.0 µF)
29. Two concentric spherical shells, with radii 10 cm and 5.0 cm, are charged to a potential difference of
20 V. How much energy is stored in this spherical capacitor? (Ans: 2.2×10-9 J)
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Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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30. In figure 16, a capacitor of capacitance C = 9.0 µF is charged to a potential difference V o = 10.0 V. The
charging battery is disconnected and the capacitor is connected to an uncharged capacitor of unknown
capacitance C x . The potential difference across the combination is reduced to V = 3.0 V. Find the value of C x .
(Ans: 21 µF)
31. A parallel-plate capacitor has plates of area A and separation d, and is charged by a battery of a potential
difference V. If the charging battery is disconnected, what is the work required, by an external agent, to separate
the plates of the capacitor to infinite distance? [Take A = 2.0 m2, V = 12 V, d = 3.0 cm] (Ans: 42 nJ)
32. In figure 17, find the charge stored by the capacitor C 3 if the potential difference across the battery is 10.0
V. Use the values C 1 = C 2 = 2.0 µF and C 3 = 4.00 µF. (Ans: 20 µC)
33. A parallel-plate air-filled capacitor, of area 25 cm2 and plate separation of 1.0 mm, is charged to a
potential difference of 600 V. Find the energy density between the plates. (Ans: 1.6 J/m3)
34. Find the equivalent capacitance of three capacitors connected in series. Assume the three capacitors are:
C 1 = 2.00 µF, C 2 = 4.00 µF and C 3 = 8.00 µF. (Ans: 1.14 µF)
35. In figure 19, find the total charge stored by the three capacitors if the potential difference V is 10.0 V.
Assume C 1 = 10.0 µF, C 2 = 5.00 µF and C 3 = 4.00 µF. (Ans: 31.6 µC)
36. Consider the circuit shown in figure 20. If C 1 = 1 µF, C 2 = 6 µF and C 3 = 3 µF, what is the charge on C 3 ?
(Ans: 3 µC)
37. What is the equivalent capacitance between points a and b in the combination of capacitors in figure 21?
(Ans: 1.0×10-6 F)
38. A parallel combination of two capacitors, C 1 and C 2 where C 2 = 2C 1 , is connected to a battery. If the
charge accumulated on C 1 is 2.0×10-6 C and the total energy stored in the combination is 12.0×10-9 J, what is the
capacitance of C 2 ? (Ans: 1.0×10-3 F)
39. An isolated conducting sphere whose radius R is 2.00 cm has a charge q = 16.0×10-9 C. What is the energy
density at the surface of the sphere? (Ans: 0.57 J/m3)
40. A parallel-plate capacitor whose capacitance is 20 pF is charged by a battery to a potential difference of
10 V between its plates. The battery is now disconnected and a dielectric slab (κ= 5) is slipped between the
plates. What is the potential energy of the capacitor after the slab is inserted? (Ans: 200 pJ)
41. Three capacitors are arranged as shown in figure 22. C 1 has a capacitance of 5.00 pF, C 2 has a
capacitance of 10.0 pF, and C 3 has a capacitance of 15.0 pF. Find the charge stored in capacitor C 1 if the
voltage drop across C 2 is 311 V. (Ans: 7.78 nC)
42. Each of the three 25-μF capacitors shown in figure 23 is initially uncharged. How much charge is stored
in the combination after the switch S is closed? (Ans: 0.30 C)
43. Find the equivalent capacitance between the points A and B in figure 24. (Ans: 4.8 µF)
44. A 10.0-µF capacitor is charged to a potential difference of 10.0 V. A 5.00-µF capacitor is charged to a
potential difference of 5.00 V. The two charged capacitors are then connected to each other in parallel with
positive plate connected to positive plate and negative plate connected to negative plate. What is the final
common potential difference between the plates of each capacitor? (Ans: 8.33 V)
45. A parallel-plate capacitor has a voltage V = 6.0 V between its plates. Each plate carries a surface charge
density σ = 7.0 nC/m2. What is the separation of the plates? (Ans: 7.6 mm)
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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46. A 6-µF air-filled capacitor is connected across a 100-V battery. After the capacitor is fully charged, it is
immersed in transformer oil (dielectric constant = 4.5). How much additional charge flows from the battery if it
remains connected during the immersion process? (Ans: 2.1 mC)
47. Capacitor C 1 is connected to a battery and charged to 4.0 × 10−8 C. It is then disconnected from the
battery and connected to two capacitors C 2 and C 3 , as shown in figure 25. The charge on the positive plate of C 1
is 1.0 × 10−8 C. What are the charges on the positive plates of C 2 and C 3 , respectively?
(Ans: q 2 = 3.0 × 10−8 C and q 3 = 3.0 × 10−8C)
48. A parallel-plate capacitor has a plate area of 0.20 m2 and a plate separation of 0.10 mm. To obtain an
electric field of 2.0×106 N/C between the plates, what should be the magnitude of the charge on each plate?
(Ans: 3.5×10-6 C)
49. Figure 10 shows an arrangement of four capacitors, 500 µF each with air between the plates. When the
space between the plates of each capacitor is filled with a material of dielectric constant 2.50, the voltmeter
reads 1000 V. What is the magnitude of the charge on each capacitor plate? (Ans: 1.25 C)
50. What is the voltage on the 2 µF capacitor shown in figure 26? (Ans: 8.9 V)
51. A 10.0-µF capacitor is charged so that the potential difference between its plates is 10.0 V. A 5.0-µF
capacitor is similarly charged so that the potential difference between its plates is 5.0 V. The two charged
capacitors are then connected to each other in parallel (positive plate connected to positive plate and negative
plate connected to negative plate). How much charge flows from one capacitor to the other when the capacitors
are connected? (Ans: 17 µC)
52. Three capacitors, each with capacitance C, are connected to a 10-V battery, as shown in figure 27. If the
charge on the first capacitor is 2.0 μC, what is its capacitance C? (Ans: 0.6 µF)
53. Two capacitors, C 1 = 16 μF and C 2 = 4.0 μF are connected in parallel and charged with a 50 V power
supply. What potential difference would be required across the same capacitors connected in series so that the
combination stores the same energy as when connected in parallel? (Ans: 125 V)
54. Two parallel plate capacitors each with a capacitance of 2.0 μF are connected in parallel to an 18-V
battery. One of the capacitors is then squeezed so that its plate separation is halved. What is the additional
charge transferred to the capacitors by the battery as a result of the squeezing? (Ans: 36 μC)
55. Two conductors, insulated from each other, are charged by transferring electrons from one conductor to
the other. After 2.5 × 1012 electrons have been transferred, the potential difference between the conductors is
12 V. What is the capacitance of the system? (Ans: 33 nF)
56. A 20-V battery is connected to a series of N capacitors, each of capacitance 4.0 µF. If the total energy
stored in the capacitors is 50 µJ, what is N? (Ans: 16)
57. A 100 V battery is connected across a combination of n capacitors connected in series. The capacitance
of each capacitor is 5.00 µF. If the total stored energy is 50 µJ, what is n? (ans: 500)
58. Consider the circuit of identical capacitors shown in figure 28. A potential difference of 2.0×102 V is
applied by the battery V. Calculate the energy stored in the system if the capacitance of each capacitor is 50 µF.
(Ans: 3.0 J)
59. Two capacitors C 1 = 10 µF and C 2 = 50 µF are connected in series. The maximum potential difference
that can be applied to each capacitor without failure is 200 V. What is the maximum energy that can be stored in
the combination? (Ans: 0.24 J)
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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60. An isolated parallel-plate capacitor stores an energy of 3.4 J. How much work is required by an external
agent to insert a dielectric of dielectric constant κ = 2.8 between the plates of the capacitor? (Ans: – 2.2 J)
61. The space between the plates a parallel-plate capacitor is filled with plastic of dielectric constant κ 1 =
2.10. The potential difference between the plates is 600 V. With the charge of the capacitor held fixed, the
plastic is replaced with glass whose dielectric constant is κ 2 = 3.40. What is the potential difference between the
capacitor after inserting the glass? (Ans: 371 V)
A B C D E
Conceptual Problems
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1. You are to connect capacitors C 1 = C and C 2 = 2C to the same battery, first individually, then in series and
then in parallel. In which of the following cases, the charge stored is the smallest?
A. C 1 and C 2 in series.
B. C 1 and C 2 in parallel.
C. C 1 individually.
D. C 2 individually.
E. In all cases the same amount of charge is stored.
2. Consider three identical capacitors. Their equivalent capacitance when connected in parallel is C p , and their
equivalent capacitance when connected in series is C s . Which of the following statements is correct?
A. C p = 9 C s
B. C p = 3 C s
C. C p = C s /9
D. C p = C s /3
E. C p = C s /2
3. A 2-μF and a 1-μF capacitors are connected in parallel and a potential difference is applied across the
combination. The 2-μF capacitor has:
A. twice the charge of the 1-μF capacitor.
B. half the charge of the 1-μF capacitor.
C. twice the potential difference of the 1-μF capacitor.
D. half the potential difference of the 1-μF capacitor.
E. none of the other answers
4. Two parallel-plate capacitors are connected in series to a battery, as shown in figure 6. A dielectric is
inserted in capacitor C 1 . Which of the following statements is correct?
A. The charge on C 2 increases.
B. The charge on C 2 increases or decreases depending on the value of the voltage of the
battery.
C. The charge on C 2 remains the same.
D. The charge on C 2 increases or decreases depending on the value of the dielectric
constant of the dielectric.
E. The charge on C 2 decreases.
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Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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5. A parallel-plate capacitor has an area A and a separation d. Find its capacitance if it is filled with two
dielectrics, as shown in figure 18. [C o is the capacitance of the air-filled parallel-plate capacitor, κ 1 = 3 and κ 2 =
1.5 are the dielectric constants]
A. 2C o
B. 6C o
C. 3C o
D. 4C o
E. C o
6. Two capacitors, C 1 and C 2 , are connected in series and a potential difference is applied to the combination.
If the capacitor that is equivalent to the combination has the same potential difference, then the charge on the
equivalent capacitors is the same as:
A. The charge on C 1 or C 2 .
B. The sum of the charges on C 1 and C 2 .
C. The difference of the charges on C 1 and C 2 .
D. The product of the charges on C 1 and C 2 .
E. The ratio of the charges on C 1 and C 2 .
7. A 2-µF and a 1-µF capacitor are connected in series and a potential difference is applied across the
combination. The 2-µF capacitor has:
A. half the potential difference of the 1-µF capacitor.
B. twice the charge of the 1-µF capacitor.
C. half the charge of the 1-µF capacitor.
D. twice the potential difference of the 1-µF capacitor.
E. zero of stored energy.
8. Consider an isolated capacitor of capacitance C o and charge Q o . Which of the following statements is true
when a dielectric slab is inserted between the plates of the capacitor?
A. The charge on the capacitor does not change.
B. The capacitance goes to zero.
C. The potential difference across the capacitor does not change.
D. The capacitance of the capacitor does not change.
E. The energy stored in the capacitor does not change.
9. Two capacitors: C 1 = 2 μF and C 2 = 1 μF are connected in parallel. A constant voltage of 10 V is applied
across both capacitors. Which of the following statements is correct?
A. Energy stored in C 1 is twice the energy stored in C 2 .
B. The potential difference across C 1 is half the potential difference across C 2 .
C. The charge on C 1 is half the charge on C 2 .
D. The energy stored in both capacitors is the same.
E. Energy stored in C 1 is half the energy stored in C 2 .
10. A parallel-plate capacitor of capacitance C has a charge of magnitude q when connected to a battery of
potential difference V. After being fully charged, the capacitor is disconnected from the battery and the
separation between the plates is doubled. Which one of the following statements is true?
A. The voltage across the plates doubles.
B. The voltage across the plates is halved.
C. The voltage across the plates remains the same.
D. The charge on the capacitor doubles.
E. The charge on the capacitor is halved.
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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11. A parallel plate capacitor is charged using a battery. While the battery is connected, a dielectric is inserted
filling completely the space between the plates. Which of the following statements is correct?
A. The stored energy will increase.
B. The electric field will increase.
C. The charge will decrease.
D. The energy density will remain constant.
E. The potential difference between the plates will increase.
12. A parallel-plate capacitor is charged by a battery and then the battery is removed and a dielectric of
dielectric constant κ is used to completely fill the gap between the plates. Inserting the dielectric changes the
energy stored in the capacitor by a factor of:
A. 1/κ
B. κ
C. κ +1
D. κ – 1
E. No change
13. A capacitor is charged using a battery, and the energy stored in it is U i . The battery is disconnected and
then the charged capacitor is connected to an identical uncharged capacitor. The energy stored by the two
capacitors is U f . Which of the following is correct?
A. U f = U i /2
B. U f = U i
C. U f = U i /4
D. U f = 4U i
E. U f = 2U i
14. The plates of a parallel-plate capacitor are connected to a battery. If the distance between the plates is
halved, the energy stored in the capacitor:
A. Increases two-fold
B. Increases four-fold
C. Remains constant
D. Reduces to one-half
E. Reduces to one-fourth
15. One of the materials listed below is to be placed between two identical metals sheets, of area A, with no
air gap, to form a parallel-plate capacitor. Which of the following materials will produce the greatest
capacitance?
A. a material of thickness 0.5 mm and dielectric constant 11.
B. a material of thickness 0.2 mm and dielectric constant 3.
C. a material of thickness 0.3 mm and dielectric constant 2.
D. a material of thickness 0.5 mm and dielectric constant 8.
E. a material of thickness 0.2 mm and dielectric constant 2.
16. A parallel-plate capacitor is fully charged to potential V. A dielectric with dielectric constant κ = 4 is
inserted between the plates of the capacitor while the potential difference between the plates remains constant.
Which one of the following statements is incorrect?
A. The electric field between the plates increases by a factor of four.
B. The energy density remains unchanged.
C. The capacitance increases by a factor of four.
D. The stored energy increases by a factor of four.
E. The charge on the capacitor increases by a factor of four.
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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17. A battery is used to charge a parallel-plate capacitor. The battery is disconnected, and then, the plates are
pulled apart to twice their original separation. This process will double the:
A. stored energy
B. capacitance
C. charge on each plate
D. surface charge density on each plate
E. electric field between the plates
18. A parallel-plate capacitor is connected to a battery that has a constant voltage. If the capacitor plates are
pulled apart (while still connected to the battery)
A. Both the electric field and the charge on the plates decrease.
B. The electric field remains constant, and the charge on the plates decreases.
C. Both the electric field and the charge on the plates increase.
D. The electric field decreases, and the charge on the plates remains constant.
E. Both the electric field and the charge on the plates remain constant.
19. Two parallel-plate capacitors with the same capacitance but different plate separation are connected in
series to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors
when they are fully charged is:
A. The electric field between the plates
B. The stored energy
C. The potential difference
D. The charge on the positive plate
E. The dielectric constant
20. Complete the following statement: When an insulator with dielectric constant κ is inserted between the
plates of a charged isolated capacitor:
A. the electric field between the plates is reduced by a factor of κ.
B. the capacitance is reduced by a factor κ.
C. the charge on the plates is reduced by a factor of κ.
D. the charge on the plates is increased by a factor of κ.
E. the potential difference between the plates is increased by a factor of κ.
21. Which of the following statements is TRUE?
A. The capacitance depends on the geometry of the capacitor.
B. The capacitance does not depend on the material separating the charged conductors.
C. The energy stored in a capacitor does not change by changing its potential.
D. Capacitors do not store energy.
E. The capacitance of a capacitor doubles when the voltage across it is doubled.
22. Consider an isolated charged parallel plate capacitor. If the plate separation is decreased while the plate
area is fixed, which of the following quantities will decrease?
A. the energy stored by the capacitor
B. the charge on the capacitor
C. the capacitance of the capacitor
D. the electric field between the plates
E. the energy density of the electric field
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Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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23. A 2-µF and a 1-µF capacitor are connected in series and charged by a battery. They store charges P and Q,
respectively. When disconnected and charged separately using the same battery, they have charges R and S,
respectively. Then:
A. R > S > P = Q
B. P > Q > R = S
C. R > P > S = Q
D. R > Q > S = P
E. S > R > P = Q
24. A parallel plate capacitor is connected to a battery. The capacitor has a certain energy density. While the
battery is still connected to the capacitor, and the distance between the capacitor plates is doubled, the capacitor
energy density
A. decreases by a factor of four.
B. increases by a factor of four.
C. increases by a factor of two.
D. decreases by a factor of two.
E. does not change.
25. Two capacitors are identical except that one is filled with air and the other is filled with oil. Both
capacitors carry the same charge. If E air refers to the electric field inside the capacitor filled with air, and E oil
refers to the electric field inside the capacitor filled with oil, then the ratio of the electric fields E air /E oil will be:
A. greater than 1
B. less than 1
C. 0
D. 1
E. None of the other answers
26. Figure 29 shows three circuits, each consisting of a switch S and two capacitors, initially charged as
indicated (top plate positive). After the switches have been closed, rank the charge on the right capacitor,
GREATEST FIRST.
A. 1 and 2 tie, then 3
B. 2, 1, 3
C. All tie
D. 3, 2, 1
E. 3, 1, 2
27. When the potential difference between the plates of a parallel-plate capacitor is V, the energy density in
the capacitor is u. If the potential difference is doubled, which of the following changes would keep the energy
density equal to its previous value u?
A. doubling the spacing between the plates
B. doubling the area of the plates
C. reducing the area of the plates by half
D. reducing the spacing between the plates
E. The energy density is unaffected by a change in the potential difference.
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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Figure 1
Figure 2
Figure 3
Figure 4
Figure 7
Figure 10
Figure 14
Figure 5
Figure 6
Figure 8
Figure 11
Figure 15
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
Figure 9
Figure 12
Figure 13
Figure 16
Figure 17
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Figure 18
Figure 19
Figure 21
Figure 24
Figure 28
Figure 20
Figure 22
Figure 25
Figure 23
Figure 26
Figure 27
Figure 29
Dr. M. F. Al-Kuhaili – PHYS 102 – Chapter 25
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