Deck 4: Capacitance

Question 1

In which of these configurations is (are) the electric field(s) uniform?

A) 1
B) 2
C) 3
D) 1 and 3
E) 1, 2, and 3

Answer 1

1

Question 2

Two flat parallel plates are d = 0.40 cm apart. The potential difference between the plates is 360 V. The electric field at the point P at the center is approximately

A) 90 kN/C
B) 3.6 kN/C
C) 0.9 kN/C
D) zero
E) 3.6 *10⁵ N/C

Answer 2

90 kN/C

Question 3

Which of the following statements about parallel plate capacitor is false?

A) The two plates have equal charges.
B) The capacitor store charges on the plates.
C) The capacitance is proportional to the area.
D) The capacitance is inversely proportional to the separation between the plates.
E) A charged capacitor stores energy.

Answer 3

The two plates have equal charges.

Question 4

A capacitor is constructed by placing a conducting sphere of radius a concentrically inside a thin conducting spherical shell of radius b. Derive an expression for the capacitance of such a capacitor.

A)
B)
C)
D)
E) It is not possible to construct such a capacitor.

Question 5

Two large metallic plates are parallel to each other and charged. The distance between the plates is d. The potential difference between the plates is V. The magnitude of the electric field in the region between the plates and away from the edges is given by

A) d/V
B) V²/d
C) dV
D) V/d²
E) None of these is correct.

Question 6

If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled, then by what factor does the capacitance change?

A) increase by a factor of 6
B) decrease by a factor of 2/3
C) decrease by a factor of 1/6
D) increase by a factor of 3/2
E) decrease by a factor of 1/2

Question 7

If a capacitor of capacitance 2.0 µF is given a charge of 1.0 mC, the potential difference across the capacitor is

A) 0.50 kV
B) 2.0 V
C) 2.0 µV
D) 0.50 V
E) None of these is correct.

Question 8

If the area of the plates of a parallel-plate capacitor is doubled, the capacitance is

A) not changed.
B) doubled.
C) halved.
D) increased by a factor of 4.
E) decreased by a factor of 1/4.

Question 9

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm. Its capacitance for a 2 m length of the cable is approximately

A) 0.22 nF
B) 34 nF
C) 46 pF
D) 92 pF
E) 184 pF

Question 10

Which of the following statements is false?

A) In the process of charging a capacitor, an electric field is produced between its plates.
B) The work required to charge a capacitor can be thought of as the work required to create the electric field between its plates.
C) The energy density in the space between the plates of a capacitor is directly proportional to the first power of the electric field.
D) The potential difference between the plates of a capacitor is directly proportional to the electric field.
E) All of these are true.

Question 11

A parallel-plate capacitor has square plates of side 8.0 cm separated by 0.80 mm. If you charge this capacitor to 15 V, the amount of charge transferred from one plate to the other is

A) 71 nC
B) 7.1 nC
C) 1.1 pC
D) 1.1 nC
E) 7.1 pC

Question 12

You want to store 10¹⁰ excess electrons on the negative plate of a capacitor at 9.0 V. How large a capacitance must you use?

A) 0.014 µF
B) 0.18 µF
C) 0.18 nF
D) 14 pF
E) 5.6 pF

Question 13

If you increase the charge on a parallel-plate capacitor from 3 µC to 9 µC and increase the plate separation from 1 mm to 3 mm, the energy stored in the capacitor changes by a factor of

A) 27
B) 9
C) 3
D) 8
E) 1/3

Question 14

A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm. Its capacitance per unit length is approximately

A) 17 nF/m
B) 0.11 nF/m
C) 92 pF/m
D) 23 pF/m
E) 46 pF/m

Question 15

You make a homemade capacitor out of two flat circular metal plates, each of radius
5 cm, and hold them a distance of 1 cm apart. You then connect each plate to the terminals of a 6-V battery. What would be the capacitance of your capacitor?

A) 7.0 * 10^-12 F
B) 2.2 * 10^-11 F
C) 2.2 * 10^-12 F
D) 2.2 * 10^-10 F
E) 7.0 * 10^-10 F

Question 16

A capacitor of capacitance C holds a charge Q when the potential difference across the plates is V. If the charge Q on the plates is doubled to 2Q,

A) the capacitance becomes (1/2)V.
B) the capacitance becomes 2C.
C) the potential changes to (1/2)V.
D) the potential changes to 2V.
E) the potential does not change.

Question 17

Doubling the potential difference across a capacitor

A) doubles its capacitance.
B) halves its capacitance.
C) quadruples the charge stored on the capacitor.
D) halves the charge stored on the capacitor.
E) does not change the capacitance of the capacitor.

Question 18

An 80-nF capacitor is charged to a potential of 500 V. How much charge accumulates on each plate of the capacitor?

A) 4.0 * 10^-4 C
B) 4.0 *10^-5 C
C) 4.0 *10^-10 C
D) 1.6 *10^-10 C
E) 1.6 * 10^-7 C

Question 19

Doubling the potential difference across a capacitor

A) doubles its capacitance.
B) halves its capacitance.
C) quadruples the charge stored on the capacitor.
D) doubles the charge stored on the capacitor.
E) produces none of the above results.

Question 20

As the voltage in the circuit is increased (but not to the breakdown voltage), the capacitance

A) increases.
B) decreases.
C) does not change.
D) increases, decreases, or does not change, depending on the charge on the plates of the capacitor.
E) does none of these.

Question 21

If the potential difference of a capacitor is reduced by one-half, the energy stored in that capacitor is

A) reduced to one-half.
B) reduced to one-quarter.
C) increased by a factor of 2.
D) increased by a factor of 4.
E) not changed.

Question 22

The charge on each capacitor in a set of capacitors in parallel is

A) directly proportional to its capacitance.
B) inversely proportional to its capacitance.
C) independent of its capacitance.
D) the same.
E) None of these is correct.

Question 23

Use the following figure to answer the next five problems:

-You connect three capacitors as shown in the diagram below. If the potential difference between A and B is 24.5 V, what is the total energy stored in this system of capacitors if C₁ = 5.0 µF, C₂ = 4.0 µF, and C₃ = 3.0 µF?

A) 1.7 * 10^-4 J
B) 1.5 *10^-4 J
C) 2.2 *10^-5 J
D) 6.8 * 10^-4 J
E) 4.0 * 10^-4 J

Question 24

A coaxial cable consists of a wire of radius 1.0 mm and an outer conducting shell of radius 8 mm. A 20 V potential difference is applied between the wire and the shell. What is the energy stored per meter of the cable?

A) 5.35 nJ/m
B) 10.7 nJ/m
C) 2.67 nJ/m
D) 61.6 pJ/m
E) 123 pJ/m

Question 25

Use the following figure to answer the next five problems:

-You connect three capacitors as shown in the diagram. C₁ = C₃ = 2.5 $\mu$ F, and
C₂ = 5.0 $\mu$ F. A potential difference of 9.0 V is maintained between the terminals A and B. The magnitude of the charge on capacitor C₃ is approximately

A) 4.2 $\mu$ C
B) 4.8 $\mu$ C
C) 17 $\mu$ C
D) 37 $\mu$ C
E) 90 $\mu$ C

Question 26

If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled, while the charge on the capacitor remains constant, then by what factor does the energy stored in the capacitor change?

A) increase by a factor of 2
B) decrease by a factor of 2/3
C) increase by a factor of 6
D) increase by a factor of 3/2
E) decrease by a factor of 1/6

Question 27

The voltage across each capacitor in a set of capacitors in parallel is

A) directly proportional to its capacitance.
B) inversely proportional to its capacitance.
C) independent of its capacitance.
D) the same.
E) None of these is correct.

Question 28

If 20 capacitors, each of 100 $\mu$ F, were connected in parallel across a 12-V battery, what would be the total energy stored in the capacitors?

A) 2.9 * 10^-1 J
B) 7.2 * 10^-3 J
C) 1.2 * 10^-2 J
D) 1.4 *10^-1 J
E) 3.6 * 10^-4 J

Question 29

You attach a 30-pF capacitor across a 1.5-V battery. How much energy is stored in the capacitor?

A) 3.4 * 10^-11 J
B) 4.5 * 10^-11 J
C) 6.7 * 10^-11 J
D) 3.4 * 10^-8 J
E) 4.5 * 10^-8 J

Question 30

Use the following figure to answer the next five problems:

-You connect three capacitors as shown in the diagram. C₁ = 5.0 $\mu$ F, C₂ = 4.0 $\mu$ F, and
C₃ = 3.0 $\mu$ F. If you apply 12 V between points A and B, the energy stored in C₃ will be approximately

A) 0.16 mJ
B) 41 $\mu$ J
C) 0.12 mJ
D) 0.41 mJ
E) 16 mF

Question 31

A coaxial cable has the inner wire of radius a = 1 mm and the outside shield of radius
B = 8 mm. The electric field strength between the wire and the shield is given by . The electrostatic energy per meter of the cable is

A) 0.328 nJ
B) 6.69 $\mu$ J
C) 3.34 $\mu$ J
D) 14.5 $\mu$ J
E) zero

Question 32

You charge a 4.0-µF capacitor to 150 V. How much additional energy must you add to charge it to 300 V?

A) 0.60 mJ
B) 0.14 J
C) 18 µJ
D) 0.30 mJ
E) 0.28 J

Question 33

The energy stored in a capacitor is directly proportional to

A) the voltage across the capacitor.
B) the charge on the capacitor.
C) the reciprocal of the charge on the capacitor.
D) the square of the voltage across the capacitor.
E) None of these is correct.

Question 34

A parallel plate capacitor is constructed using two square metal sheets, each of side
L = 10 cm. The plates are separated by a distance d = 2 mm and a voltage applied between the plates. The electric field strength within the plates is E = 4000 V/m. The energy stored in the capacitor is

A) 0.71 nJ
B) 1.42 nJ
C) 2.83 nJ
D) 3.67 nJ
E) zero

Question 35

You connect three capacitors as shown in the diagram. C₁ = C₃ = 2.5 $\mu$ F, and
C₂ = 5.0 $\mu$ F. A potential difference of 9.0 V is maintained between the terminals A and B. The voltage across on capacitor C₃ is approximately

A) 1.2 V
B) 7.9 V
C) 3.2 V
D) 5.4 V
E) 6.8 V

Question 36

A coaxial cable consists of a wire of radius 1.0 mm and an outer conducting shell of radius 8 mm. A 20 V potential difference is applied between the wire and the shell. What is the energy stored in a 2 m length of the cable?

A) 5.35 nJ
B) 10.7 nJ
C) 2.67 nJ
D) 61.6 pJ
E) 123 pJ

Question 37

A 2.0-µF capacitor has a potential difference of 5000 V. The work done in charging it was

A) 2.5 J
B) 5.0 J
C) 25 J
D) 5.0 mJ
E) 0.50 kJ

Question 38

Use the following figure to answer the next five problems:

-You connect three capacitors as shown in the diagram below. The effective capacitance of this combination when C₁ = 5.0 $\mu$ F, C₂ = 4.0 $\mu$ F, and C₃ = 3.0 $\mu$ F is approximately

A) 0.44 $\mu$ F
B) 2.3 $\mu$ F
C) 3.5 $\mu$ F
D) 5.2 $\mu$ F
E) 12 $\mu$ F

Question 39

A cardiac defibrillator can be used to help an erratic heartbeat in a regular fashion. A defibrillator contains a capacitor charged to a voltage of 6000 V with an energy storage of 200 J. Calculate the capacitance of the capacitor.

A) 6.67 * 10^-2 F
B) 1.11 *10^-5 F
C) 5.56 *10^-6 F
D) 2.22 * 10^-5 F
E) 13.3 F

Question 40

If you decrease the charge on a parallel-plate capacitor from 12 µC to 4 µC and increase the plate separation from 1 mm to 3 mm, the energy stored in the capacitor changes by a factor of

A) 27
B) 1/3
C) 3
D) 8
E) 1/4

Question 41

A capacitor, C₁ = 5.0 $\mu$ F, is charged up to 8 V. It is then connected to a second uncharged capacitor C₂ = 2.5 $\mu$ F. The charge on C₁ after the system has come to equilibrium is

A) 26.7 $\mu$ C
B) 13.3 $\mu$ C
C) 20.0 $\mu$ C
D) 40.0 $\mu$ C
E) 6.67 $\mu$ C

Question 42

When you insert a piece of paper ( $\kappa$ = 3.7) into the air between the plates of a capacitor, the capacitance

A) increases.
B) decreases.
C) does not change.
D) could increase, decrease, or not change depending on the dielectric constant of the paper.
E) does none of these.

Question 43

You connect two capacitors C₁ = 15 pF and C₂ = 30 pF in series across a 1.5-V battery. The potential difference across capacitor C₁ is approximately

A) 0.50 V
B) 1.0 V
C) 1.5 V
D) 0.33 V
E) 0.67 V

Question 44

The equivalent capacitance of two capacitors in series is

A) the sum of their capacitances.
B) the sum of the reciprocals of their capacitances.
C) always greater than the larger of their capacitances.
D) always less than the smaller of the capacitances.
E) described by none of the above.

Question 45

A capacitor, C₁ = 5.0 $\mu$ F, is charged up to 8 V. It is then connected to a second uncharged capacitor C₂ = 2.5 $\mu$ F. The voltage across the capacitor C₁ after the system has come to equilibrium is

A) 2.67 V
B) 4.0 V
C) 5.33 V
D) 8.0 V
E) 12.0 V

Question 46

A 1.0- $\mu$ F capacitor and a 2.0- $\mu$ F capacitor are connected in series across a 1200-V source. The charge on each capacitor is

A) 0.40 mC
B) 0.80 mC
C) 1.2 mC
D) 1.8 mC
E) 3.6 mC

Question 47

If C₁ < C₂ < C₃ < C₄ for the combination of capacitors shown, the equivalent capacitance

A) is less than C₁.
B) is more than C₄.
C) is between C₂ and C₃.
D) is more than C₂.
E) could be any value depending on the applied voltage.

Question 48

The equivalent capacitance of three capacitors in series is

A) the sum of their capacitances.
B) the sum of the reciprocals of their capacitances.
C) always greater than the larger of their capacitances.
D) always less than the smaller of the capacitances.
E) described by none of the above.

Question 49

The equivalent capacitance of two capacitors in parallel is

A) the sum of the reciprocals of their capacitances.
B) the reciprocal of the sum of the reciprocals of their capacitances.
C) always greater than the larger of their capacitances.
D) always less than the smaller of the two capacitances.
E) described by none of the above.

Question 50

The charge on each capacitor in a set of capacitors in series is

A) directly proportional to its capacitance.
B) inversely proportional to its capacitance.
C) independent of its capacitance.
D) the same.
E) None of these is correct.

Question 51

The voltage across each capacitor in a set of capacitors in series is

A) directly proportional to its capacitance.
B) inversely proportional to its capacitance.
C) independent of its capacitance.
D) the same.
E) None of these is correct.

Question 52

The equivalent capacitance of three capacitors in parallel is

A) the sum of the reciprocals of their capacitances.
B) the reciprocal of the sum of the reciprocals of their capacitances.
C) always greater than the larger of their capacitances.
D) always less than the smaller of the two capacitances.
E) described by none of the above.

Question 53

If all the four capacitors have equal values of 50 $\mu$ F then calculate the equivalent capacitance of the circuit shown above.

A) 50 $\mu$ F
B) 30 $\mu$ F
C) 75 $\mu$ F
D) 100 $\mu$ F
E) 83 $\mu$ F

Question 54

A capacitor, C₁ = 5.0 $\mu$ F, is charged up to 8 V. It is then connected to a second uncharged capacitor C₂ = 2.5 $\mu$ F. The charge on C₂ after the system has come to equilibrium is

A) 26.7 $\mu$ C
B) 13.3 $\mu$ C
C) 20.0 $\mu$ C
D) 40.0 $\mu$ C
E) 6.67 $\mu$ C

Question 55

You connect two 12- $\mu$ F capacitors and a 6- $\mu$ F capacitor in parallel. The equivalent capacitance of the combination is

A) 18 $\mu$ F
B) 4 $\mu$ F
C) 3 $\mu$ F
D) 30 $\mu$ F
E) None of these is correct.

Question 56

The capacitance of a parallel-plate capacitor

A) is defined as the amount of work required to move a charge from one plate to the other.
B) decreases if a dielectric is placed between its plates.
C) is independent of the distance between the plates.
D) has units of J/C.
E) is independent of the charge on the capacitor.

Question 57

A capacitor is made with two strips of metal foil, each 2.5 cm wide by 50 cm long, with a 0.70- $\mu$ m thick strip of paper ( $\kappa$ = 3.7) sandwiched between them. The capacitor is rolled up to save space. What is the capacitance of this device? (The permittivity of free space $\epsilon$ ₀ = 8.85 *10^-12 F/m.)

A) 43 nF
B) 0.16 $\mu$ F
C) 0.58 $\mu$ F
D) 2.0 $\mu$ F
E) 7.3 $\mu$ F

Question 58

If C₁ < C₂ < C₃ < C₄ for the combination of capacitors shown, the equivalent capacitance

A) is less than C₁.
B) is more than C₄.
C) is between C₂ and C₃.
D) is less than C₂.
E) could be any value depending on the applied voltage.

Question 59

Three capacitors 2 $\mu$ F, 4 $\mu$ F and 8 $\mu$ F are connected in parallel across a 120-V source. The charge on the 4 $\mu$ F capacitor is

A) 2.4 * 10^-4 C
B) 9.6 * 10^-4 C
C) 2.1 * 10³ C
D) 1.7 * 10^-3 C
E) 4.8 * 10^-4 C

Question 60

You want to use three capacitors in a circuit. If each capacitor has a capacitance of 3 pF, the configuration that gives you an equivalent capacitance of 2 pF between points x and y is

A) 1
B) 2
C) 3
D) 4
E) None of these is correct.

Question 61

A capacitor is connected to a battery as shown. When a dielectric is inserted between the plates of the capacitor,

A) only the capacitance changes.
B) only the voltage across the capacitor changes.
C) only the charge on the capacitor changes.
D) both the capacitance and the voltage change.
E) both the capacitance and the charge change.

Question 62

A parallel-plate capacitor has square plates of side 12 cm and a separation of 6.0 mm. A dielectric slab of constant $\kappa$ = 2.0 has the same area as the plates but has a thickness of 3.0 mm. What is the capacitance of this capacitor with the dielectric slab between its plates?

A) 28 pF
B) 21 pF
C) 16 pF
D) 37 pF
E) 53 pF

Question 63

The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon ( $\kappa$ = 4.2). A potential difference of 20 V is maintained between the wire and the shield. The energy stored per meter of the cable is

A) 1.12 nJ/m
B) 22.5 nJ/m
C) 44.9 nJ/m
D) 5.36 nJ/m
E) 2.68 nJ/m

Question 64

A parallel plate capacitor has a plate spacing of 1.5 mm, which is filled with a dielectric of $\kappa$ = 4.3, and its capacitance is 80 $\mu$ F. If the dielectric is taken out and the plate spacing doubled, then what is the new capacitance?

A) 690 $\mu$ F
B) 37 $\mu$ F
C) 9.3 $\mu$ F
D) 170 $\mu$ F
E) 19 $\mu$ F

Question 65

If a dielectric is inserted between the plates of a parallel-plate capacitor that is connected to a 100-V battery, the

A) voltage across the capacitor decreases.
B) electric field between the plates decreases.
C) electric field between the plates increases.
D) charge on the capacitor plates decreases.
E) charge on the capacitor plates increases.

Question 66

Two identical capacitors A and B are connected across a battery, as shown. If mica ( $\kappa$ = 5.4) is inserted in B,

A) both capacitors will retain the same charge.
B) B will have the larger charge.
C) A will have the larger charge.
D) the potential difference across B will increase.
E) the potential difference across A will increase.

Question 67

The capacitance of a parallel-plate capacitor is 24 $\mu$ F when the plates are separated by a material of dielectric constant 2.0. If this material is removed, leaving air between the plates, and the separation between the plates is tripled, the capacitance is

A) unchanged
B) 16 $\mu$ F
C) 36 F $\mu$ F
D) 0.14 mF
E) 4.0 $\mu$ F

Question 68

A potential of 12 V is applied across a parallel-plate capacitor which is constructed of square plates of side 10 cm and separation of 4.0 mm. A dielectric slab of constant
$\kappa$ = 2.5 is inserted between the plates so that it completely fills the space. What is the bound surface charge density on the dielectric?

A) 12.3 pC/m²
B) 15.9 pC/m²
C) 39.8 pC/m²
D) 56.8 pC/m²
E) 85.4 pC/m²

Question 69

A charged capacitor has an initial electric field ₀ and potential difference V₀ across its plates. Without connecting any source of emf, you insert a dielectric ( $\kappa$ > 1) slab between the plates to produce an electric field _d and a potential difference V_d across the capacitor. The pair of statements that best represents the relationships between the electric fields and potential differences is

A) _d > ₀; V_d > V₀
B) _d = ₀; V_d > V₀
C) _d > ₀; V_d = V₀
D) _d < ₀; V_d > V₀
E) _d < ₀; V_d < V₀

Question 70

Two parallel plate air capacitors, each of capacitance X F are in series with a battery of 12-V. If a dielectric with $\kappa$ = 3 is inserted between the plates of one of the capacitors, then calculate the change in electrical charge (in Coulombs) that occurs on one of its plates.

A) 9X
B) 3X/4
C) 3X
D) 16X
E) none of the above

Question 71

The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon ( $\kappa$ = 4.2). The capacitance per meter is

A) 13.4 pF
B) 26.8 pF
C) 35.8 pF
D) 56.2 pF
E) 112 pF

Question 72

A parallel plate capacitor of area A = 30 cm² and separation d = 5 mm is charged by a battery of 60-V. If the air between the plates is replaced by a dielectric of $\kappa$ = 4 with the battery still connected, then what is the ratio of the initial charge on the plates divided by the final charge on the plates?

A) 4.3
B) 1
C) 16
D) 0.25
E) 4.0

Question 73

An electric field, E, is applied to a dielectric. Which of the following statements is true?

A) The electric field within the dielectric is less than E.
B) The dielectric produces an electric field in the opposite direction to E.
C) The molecules in the dielectric become polarized.
D) The electric field will produce a torque on molecules in dielectrics which have permanent dipoles.
E) All the above statements are true.