Question 1

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network?

Accepted Answer

A)  20 µF 
B)  3.0 µF 
C)  10 µF 
D)  5.0 µF 
E)  1.0 µF 
A)  20 µF 
B)  3.0 µF 
C)  10 µF 
D)  5.0 µF 
E)  1.0 µF

Question 2

In the circuit shown in the figure, the capacitors are initially uncharged. The switch is first thrown to position A and kept there for a long time. It is then thrown to position B. Let the charges on the capacitors be Q1, Q2, and Q3 and the potential differences across them be V1, V2, and V3. Which of the following conditions must be true with the switch in position B?

Accepted Answer

A)  V1 = V2 = V3 
B)  V1 + V2 = V3 
C)  V3 = V0 
D)  Q1 = Q2 = Q3 
E)  Q1 + Q2 = Q3 
A)  V1 = V2 = V3 
B)  V1 + V2 = V3 
C)  V3 = V0 
D)  Q1 = Q2 = Q3 
E)  Q1 + Q2 = Q3

Question 3

A parallel-plate capacitor consists of two parallel, square plates that have dimensions 1.0 cm by 1.0 cm. If the plates are separated by 1.0 mm, and the space between them is filled with teflon, what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1, and ε0 = 8.85 × 10-12 C2/N ∙ m2.)

Accepted Answer

A)  1.9 pF 
B)  0.44 pF 
C)  2.1 pF 
D)  0.89 pF 
A)  1.9 pF 
B)  0.44 pF 
C)  2.1 pF 
D)  0.89 pF

Question 4

Four capacitors are connected across a 90-V voltage source as shown in the figure.   
(a) What is the charge on the 4.0-μF capacitor?
(b) What is the charge on a 2.0-μF capacitor?
(c) What is the charge on the 3.0-μF capacitor?
(d) What is the potential difference across the 6.0-μF capacitor?

Accepted Answer

(a) 120 µC

Question 5

The four identical capacitors in the circuit shown in the figure are initially uncharged. Let the charges on the capacitors be Q1, Q2, Q3, and Q4 and the potential differences across them be V1, V2, V3, and V4. The switch is thrown first to position A and kept there for a long time. It is then thrown to position B. Which of the following conditions is true with the switch in position B?

Accepted Answer

A)  V1 = V2 = V3 = V4 
B)  V1 = V0 
C)  V1 + V2 + V3 + V4 = V0 
D)  Q1 = 3 Q2 
E)  Q1 = Q2 
A)  V1 = V2 = V3 = V4 
B)  V1 = V0 
C)  V1 + V2 + V3 + V4 = V0 
D)  Q1 = 3 Q2 
E)  Q1 = Q2

Question 6

A parallel-plate capacitor has plates of area 0.40 m2 and plate separation of 0.20 mm. The capacitor is connected across a 9.0-V potential source. (ε0 = 8.85 × 10-12 C2/N ∙ m2)
(a) What is the magnitude of the electric field between the plates?
(b) What is the capacitance of the capacitor?
(c) What is the magnitude of the charge on each plate of the capacitor?

Accepted Answer

(a) 4.5 ×

Question 7

A parallel-plate capacitor, with air between the plates, is connected across a voltage source. This source establishes a potential difference between the plates by placing charge of magnitude 4.15 × 10-6 C on each plate. The space between the plates is then filled with a dielectric material, with a dielectric constant of 7.74. What must the magnitude of the charge on each capacitor plate now be, to produce the same potential difference between the plates as before?

Accepted Answer

Question 8

Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm2. How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε00 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  56 pC 
B)  39 pC 
C)  78 pC 
D)  3.5 µC 
A)  56 pC 
B)  39 pC 
C)  78 pC 
D)  3.5 µC

Question 9

An air-filled parallel-plate capacitor is connected to a battery and allowed to charge up. Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery. After this is done, we find that

Accepted Answer

A)  the energy stored in the capacitor had decreased. 
B)  the voltage across the capacitor had increased. 
C)  the charge on the capacitor had increased. 
D)  the charge on the capacitor had not changed. 
E)  None of these choices are true. 
A)  the energy stored in the capacitor had decreased. 
B)  the voltage across the capacitor had increased. 
C)  the charge on the capacitor had increased. 
D)  the charge on the capacitor had not changed. 
E)  None of these choices are true.

Question 10

The charge on the square plates of a parallel-plate capacitor is Q. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The amount of charge on the plates is now equal to

Accepted Answer

A)  4Q. 
B)  2Q. 
C)  Q. 
D)  Q/2. 
E)  Q/4. 
A)  4Q. 
B)  2Q. 
C)  Q. 
D)  Q/2. 
E)  Q/4.

Question 11

A charged capacitor stores energy U. Without connecting this capacitor to anything, dielectric having dielectric constant K is now inserted between the plates of the capacitor, completely filling the space between them. How much energy does the capacitor now store?

Accepted Answer

A)  2KU 
B)  KU 
C)  U 
D)    
E)    
A)  2KU 
B)  KU 
C)  U 
D)    
E)

Question 12

Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m2, and the separation of the plates is 0.020 mm. An electric field of 3.9 × 106 V/m is present between the plates. What is the surface charge density on the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  35 µC/m2 
B)  73 µC/m2 
C)  17 µC/m2 
D)  52 µC/m2 
E)  87 µC/m2 
A)  35 µC/m2 
B)  73 µC/m2 
C)  17 µC/m2 
D)  52 µC/m2 
E)  87 µC/m2

Question 13

When two or more capacitors are connected in parallel across a potential difference

Accepted Answer

A)  the potential difference across each capacitor is the same. 
B)  each capacitor carries the same amount of charge. 
C)  the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. 
D)  All of the above choices are correct. 
E)  None of the above choices are correct. 
A)  the potential difference across each capacitor is the same. 
B)  each capacitor carries the same amount of charge. 
C)  the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. 
D)  All of the above choices are correct. 
E)  None of the above choices are correct.

Question 14

A parallel-plate capacitor has a capacitance of 10 mF and charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. How much energy is now stored by the capacitor?

Accepted Answer

A)  250 mJ 
B)  125 mJ 
C)  500 mJ 
D)  62.5 mJ 
E)  1200 mJ 
A)  250 mJ 
B)  125 mJ 
C)  500 mJ 
D)  62.5 mJ 
E)  1200 mJ

Question 15

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m2, and the separation of the plates is 0.080 mm. An electric field of 5.3 × 106 V/m is present between the plates. What is the energy density between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

Accepted Answer

A)  124 J/m3 
B)  84 J/m3 
C)  170 J/m3 
D)  210 J/m3 
E)  250 J/m3 
A)  124 J/m3 
B)  84 J/m3 
C)  170 J/m3 
D)  210 J/m3 
E)  250 J/m3

Question 16

The electric field between square the plates of a parallel-plate capacitor has magnitude E. The potential across the plates is maintained with constant voltage by a battery as they are pulled apart to twice their original separation, which is small compared to the dimensions of the plates. The magnitude of the electric field between the plates is now equal to

Accepted Answer

A)  4E. 
B)  2E. 
C)  E. 
D)  E/2. 
E)  E/4. 
A)  4E. 
B)  2E. 
C)  E. 
D)  E/2. 
E)  E/4.

Question 17

When two or more capacitors are connected in series across a potential difference

Accepted Answer

A)  the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors. 
B)  each capacitor carries the same amount of charge. 
C)  the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. 
D)  All of the above choices are correct. 
E)  None of the above choices are correct. 
A)  the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors. 
B)  each capacitor carries the same amount of charge. 
C)  the equivalent capacitance of the combination is less than the capacitance of any of the capacitors. 
D)  All of the above choices are correct. 
E)  None of the above choices are correct.

Question 18

A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged. The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is inserted. The dielectric has a dielectric constant of 5.0.
(a) What is the capacitance of the capacitor after the slab has been inserted?
(b) What is the potential difference across the plates of the capacitor after the slab has been inserted?

Accepted Answer

The answer of A 15-μF air-filled capacitor is connected to...

Question 19

Three capacitors, with capacitances C1 = 4.0 μF, C2 = 3.0 μF, and C3 = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor C2?

Accepted Answer

A)  16 μC 
B)  32 μC 
C)  2.0 μC 
D)  8.0 μC 
E)  4.0 μC 
A)  16 μC 
B)  32 μC 
C)  2.0 μC 
D)  8.0 μC 
E)  4.0 μC

Question 20

An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

Accepted Answer

A)  0.077 mJ 
B)  468 mJ 
C)  0.040 mJ 
D)  6.00 mJ 
A)  0.077 mJ 
B)  468 mJ 
C)  0.040 mJ 
D)  6.00 mJ

Exam 23: Capacitance and Dielectrics

The capacitors in the network shown in the figure all have a capacitance of 5.0 µF. What is the equivalent capacitance, Cab, of this capacitor network?

Four capacitors are connected across a 90-V voltage source as shown in the figure. (a) What is the charge on the 4.0-μF capacitor? (b) What is the charge on a 2.0-μF capacitor? (c) What is the charge on the 3.0-μF capacitor? (d) What is the potential difference across the 6.0-μF capacitor?

Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm2. How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε00 = 8.85 × 10-12 C2/N ∙ m2)

An air-filled parallel-plate capacitor is connected to a battery and allowed to charge up. Now a slab of dielectric material is placed between the plates of the capacitor while the capacitor is still connected to the battery. After this is done, we find that

A charged capacitor stores energy U. Without connecting this capacitor to anything, dielectric having dielectric constant K is now inserted between the plates of the capacitor, completely filling the space between them. How much energy does the capacitor now store?

Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m2, and the separation of the plates is 0.020 mm. An electric field of 3.9 × 106 V/m is present between the plates. What is the surface charge density on the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

When two or more capacitors are connected in parallel across a potential difference

A parallel-plate capacitor has a capacitance of 10 mF and charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. How much energy is now stored by the capacitor?

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m2, and the separation of the plates is 0.080 mm. An electric field of 5.3 × 106 V/m is present between the plates. What is the energy density between the plates? (ε0 = 8.85 × 10-12 C2/N ∙ m2)

When two or more capacitors are connected in series across a potential difference

Three capacitors, with capacitances C1 = 4.0 μF, C2 = 3.0 μF, and C3 = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor C2?

An air-filled capacitor stores a potential energy of 6.00 mJ due to its charge. It is accidentally filled with water in such a way as not to discharge its plates. How much energy does it continue to store after it is filled? (The dielectric constant for water is 78 and for air it is 1.0006.)

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Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm². How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε₀₀ = 8.85 × 10^-12 C²/N ∙ m²)

Each plate of a parallel-plate air-filled capacitor has an area of 0.0020 m², and the separation of the plates is 0.020 mm. An electric field of 3.9 × 10⁶ V/m is present between the plates. What is the surface charge density on the plates? (ε₀ = 8.85 × 10-12 C²/N ∙ m²)

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m², and the separation of the plates is 0.080 mm. An electric field of 5.3 × 10⁶ V/m is present between the plates. What is the energy density between the plates? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Three capacitors, with capacitances C₁ = 4.0 μF, C₂ = 3.0 μF, and C₃ = 2.0 μF, are connected to a 12 -V voltage source, as shown in the figure. What is the charge on capacitor C₂?