Chapter 24: Capacitance Section 24-1: Capacitance

Chapter 24: Capacitance

Section 24-1: Capacitance

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. 180 N/C.

C. 0.9 kN/C.

D. Zero.

E. 3.6 105 N/C

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. 180 N/C.

C. 0.9 kN/C.

D. Zero.

E. 3.6 105 N/C

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 E in the region between the plates and away from the edges is given by

A. d/V.

B. V2/d.

C. d ∙V.

D. V/d2.

E. V/d.

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 E in the region between the plates and away from the edges is given by

A. d/V.

B. V2/d.

C. d ∙V.

D. V/d2.

E. V/d .

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.

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.

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.

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.

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.

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.

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

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

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

a. increases.

b. decreases.

c. does not change.

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

A. increases.

B. decreases.

C. does not change.

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.

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.

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. It increases by a factor of 6.

b. It decreases by a factor of 2/3.

c. It decreases by a factor of 1/6.

d. It increases by a factor of 3/2.

e. It decreases by a factor of ½.

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. It increases by a factor of 6.

B. It decreases by a factor of 2/3.

C. It decreases by a factor of 1/6.

D. It increases by a factor of 3/2.

E. It decreases by a factor of ½.

Chapter 24: Capacitance

Section 24-2: The Storage of Electrical Energy

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. None of these is false.

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. None of these is false.

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

a. The two plates have equal charges of the same sign.

b. The capacitor stores charges on the plates.

c. The capacitance is proportional to the area of the plates.

d. The capacitance is inversely proportional to the separation between the plates.

e. A charged capacitor stores energy.

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

A. The two plates have equal charges of the same sign.

B. The capacitor stores charges on the plates.

C. The capacitance is proportional to the area of the plates.

D. The capacitance is inversely proportional to the separation between the plates.

E. A charged capacitor stores energy.

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, but keep all other properties the same, the energy stored in the capacitor changes by a factor of

a. 27.

b. 9.

c. 3.

d. 8.

e. 1/3.

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, but keep all other properties the same, the energy stored in the capacitor changes by a factor of

A. 27.

B. 9.

C. 3.

D. 8.

E. 1/3.

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.

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.

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.

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.

Chapter 24: Capacitance

Section 24-3: Capacitors, Batteries and Circuits, and Concept Check 24-1

A circuit consists of a capacitor, a battery, and a switch, all connected in series. Initially, the switch is open and the capacitor is uncharged. The switch is then closed and the capacitor charges. While the capacitor is charging, how does the net charge within the battery change?

a. It increases.

b. It decreases.

c. It stays the same

A circuit consists of a capacitor, a battery, and a switch, all connected in series. Initially, the switch is open and the capacitor is uncharged. The switch is then closed and the capacitor charges. While the capacitor is charging, how does the net charge within the battery change?

A. It increases.

B. It decreases.

C. It stays the same

Several different capacitors are hooked across a DC battery in parallel. The charge on each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in parallel. The charge on each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in parallel. The voltage across each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in parallel. The voltage across each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in series. The charge on each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in series. The charge on each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in series. The voltage across each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

Several different capacitors are hooked across a DC battery in series. The voltage across each capacitor is

A. directly proportional to its capacitance.

B. inversely proportional to its capacitance.

C. independent of its capacitance.

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

A. less than C1.

B. more than C4.

C. between C1 and C4.

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

A. less than C1.

B. more than C4.

C. between C1 and C4.

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

A. less than C1.

B. more than C4.

C. between C1 and C4.

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

A. less than C1.

B. more than C4.

C. between C1 and C4.

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.

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.

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.

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.

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.

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.

Chapter 24: Capacitance

Section 24-4: Dielectrics

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.

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.

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.

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.

Two identical capacitors A and B are connected across a battery, as shown. If mica ( = 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.

Two identical capacitors A and B are connected across a battery, as shown. If mica ( = 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.

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.

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.

A charged capacitor has an initial electric field E0 and potential difference V0 across its plates. Without connecting any source of emf, you insert a dielectric ( > 1) slab between the plates to produce an electric field Ed and a potential difference Vd across the capacitor. The pair of statements that best represents the relationships between the magnitude of the electric fields and

potential differences is

A. Ed > E0; Vd > V0 . D. Ed < E0; Vd > V0.

B. Ed = E0; Vd > V0 . E. Ed < E0; Vd < V0.

C. Ed > E0; Vd = V0.

A charged capacitor has an initial electric field E0 and potential difference V0 across its plates. Without connecting any source of emf, you insert a dielectric ( > 1) slab between the plates to produce an electric field Ed and a potential difference Vd across the capacitor. The pair of statements that best represents the relationships between the magnitude of the electric fields and

potential differences is

A. Ed > E0; Vd > V0. D. Ed < E0; Vd > V0.

B. Ed = E0; Vd > V0. E. Ed < E0; Vd < V0.

C. Ed > E0; Vd = V0.

Chapter 24: Capacitance

Section 24-5: Molecular View of a Dielectric, and Concept Check 24-2

Does the capacitance always increase when a dielectric is inserted into the gap of a capacitor?

a. Yes, it always increases.

b. No, it always decreases.

c. No, it may increase or decrease depending on the dielectric constant of the material.

Does the capacitance always increase when a dielectric is inserted into the gap of a capacitor?

A. Yes, it always increases.

B. No, it always decreases.

C. No, it may increase or decrease depending on the dielectric constant of the material.

An external electric field, E, is applied to a region which contains 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 the dielectric that have permanent dipoles.

E. All the above statements are true.

An external electric field, E, is applied to a region which contains 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 the dielectric that have permanent dipoles.

E. All the above statements are true.