Question 1

A dielectric is inserted between the plates of an isolated parallel-plate capacitor that carries a charge Q. What happens to the potential energy stored in the capacitor?

Accepted Answer

When a dielectric is inserted into an isolated capacitor, the capacitance increases, and since the charge remains constant, the potential energy decreases.

Question 2

Three identical capacitors are connected in parallel to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

Accepted Answer

In a parallel connection, the total charge Q is distributed equally among the capacitors, so each capacitor carries Q/3 charge.

Question 3

FIGURE 24-4 -Two parallel-plate capacitors are connected in series to a battery as shown in Fig. 24-4. A dielectric is inserted in capacitor C₁. What happens to the charge on capacitor C₂?

Accepted Answer

When a dielectric is inserted into C₁, its capacitance increases, leading to an increase in the total capacitance of the series combination. Since the capacitors are in series, the charge on each capacitor must be the same, and thus the charge on C₂ increases to maintain the same voltage across the series combination.

Question 4

A parallel-plate capacitor is charged by a battery and then the battery is removed and a dielectric of constant K is used to fill the gap between the plates. Inserting the dielectric changes the energy stored by a factor of

Accepted Answer

When a dielectric is inserted into a charged capacitor (with the battery removed), the capacitance increases by a factor of K, but the charge remains constant. The energy stored in the capacitor is given by U = Q²/(2C). Since the capacitance increases by K, the energy decreases by a factor of 1/K.

Question 5

A capacitor consists of a set of two parallel plates of area A separated by a distance d. The capacitor plates carry charges +Q and -Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will

Accepted Answer

The answer of A capacitor consists of a set of...

Question 6

A parallel-plate capacitor of capacitance C is connected to a battery of voltage V until it is fully charged. The energy density in the capacitor is then equal to u. If the same capacitor is then connected to a battery of voltage 2V its energy density becomes equal to

Accepted Answer

The energy density in a capacitor is proportional to the square of the voltage (u ∝ V²). If the voltage is doubled (from V to 2V), the energy density becomes (2V)² = 4V², which is four times the original energy density.

Question 7

Capacitance of capacitors depends upon

Accepted Answer

The capacitance of a capacitor is influenced by the dielectric material between the conductors, the geometry (shape and size) of the conductors, and the distance between them.

Question 8

FIGURE 24-1 
-Fig. 24-1 shows 3 capacitors, of equal capacitance C, connected to a battery of voltage V. What is the equivalent capacitance of this combination?

Accepted Answer

The answer of FIGURE 24-1 
-Fig. 24-1 shows 3 capacitors,...

Question 9

A dielectric material such as paper is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field between the plates?

Accepted Answer

The electric field between the plates becomes weaker because the dielectric material reduces the effective electric field by polarizing and partially canceling the field created by the charges on the plates.

Question 10

FIGURE 24-3 -Three capacitors C₁, C₂, and C₃ are connected to a battery as shown in Fig. 24-3. The three capacitors have equal capacitances. Which capacitor stores the most potential energy?

Accepted Answer

The answer of FIGURE 24-3 -Three capacitors C₁, C₂, and...

Question 11

5.00 μF, 10.0 μF, and 50.0 μF capacitors are connected in series across a 12.0-V battery.
(a) How much charge is stored in the 5.00-μF capacitor?
(b) What is the potential difference across the 10.0-μF capacitor?

Accepted Answer

The answer of 5.00 μF, 10.0 μF, and 50.0 μF...

Question 12

A 15-μF capacitor is connected to a 50-V battery and becomes fully charged. The battery is 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 is inserted?
(b) What is the voltage across the capacitor's plates after the slab is inserted?

Accepted Answer

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

Question 13

A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery. (a) What is the electric field between the plates? (b) What is the capacitance of the capacitor? (c) What is the charge on the capacitor?

Accepted Answer

The answer of A parallel-plate capacitor has plates of area...

Question 14

Two capacitors of 6.00 μF and 8.00 μF are connected in parallel. The combination is then connected in series with a 12.0-V battery and a 14.0-μF capacitor.
(a) What is the equivalent capacitance?
(b) What is the charge on the 6.00-μF capacitor?
(c) What is the voltage across the 6.00-μF capacitor?

Accepted Answer

The answer of Two capacitors of 6.00 μF and 8.00...

Question 15

When a parallel-plate capacitor of capacitance C is connected to a battery of voltage V, the energy density in the capacitor is u. If the voltage of battery is doubled, which of the following changes would keep the energy density equal to its previous value u?

Accepted Answer

Doubling the spacing of the plates reduces the capacitance, which compensates for the increase in voltage, keeping the energy density the same.

Question 16

FIGURE 24-5 
-Four capacitors are connected across a 90-V DC source as shown in Fig. 24-5.
(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 voltage across the 6-μF capacitor?

Accepted Answer

The answer of FIGURE 24-5 
-Four capacitors are connected across...

Question 17

A capacitor consists of a set of two parallel plates of area A separated by a distance d. This capacitor is connected to a battery that maintains a constant potential difference between the plates. If the separation between the plates is doubled, the magnitude of the electrical energy stored on the capacitor will

Accepted Answer

The amount of energy saved in a capacitor, E, is proportional to the square of the plate separation, d, and the plate area, A. This is given by the equation E = (1/2)QV = (1/2)(CV^2) = (1/2)(εA/d)(V^2), where Q is the charge saved on the plates, C is the capacitance of the capacitor, V is the potential difference across the plates, and ε is the permittivity of the vacuum. If d is increased by a factor of 2, E will be decreased by a factor of (1/2)^2 = 1/4, as E is inversely proportional to d. Therefore, the correct answer is C.

Question 18

If the voltage on a capacitor is doubled, then the energy stored by the capacitor

Accepted Answer

The energy stored in a capacitor is given by the formula $ E = \frac{1}{2} C V^2 $. If the voltage $ V $ is doubled, the energy becomes $ \frac{1}{2} C (2V)^2 = 2^2 \times \frac{1}{2} C V^2 = 4 \times \frac{1}{2} C V^2 $, which means the energy quadruples.

Question 19

FIGURE 24-2 -Fig. 24-2 shows three capacitors connected to a battery. The capacitances are such that C₁ = 2 C₂ and C₁ = 3C₃. Which capacitor stores the smallest amount of charge?

Accepted Answer

The answer of FIGURE 24-2 
-Fig. 24-2 shows three capacitors...

Question 20

A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V battery.
(a) What is the voltage across the 1.0-μF capacitor?
(b) What is the voltage across the 2.0-μF capacitor?

Accepted Answer

The answer of A 1.0-μF and a 2.0-μF capacitor are...

Quiz 24: Capacitance, Dielectrics, Electric Energy Storage

A dielectric is inserted between the plates of an isolated parallel-plate capacitor that carries a charge Q. What happens to the potential energy stored in the capacitor?

Three identical capacitors are connected in parallel to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

FIGURE 24-4 -Two parallel-plate capacitors are connected in series to a battery as shown in Fig. 24-4. A dielectric is inserted in capacitor C1. What happens to the charge on capacitor C2?

A parallel-plate capacitor is charged by a battery and then the battery is removed and a dielectric of constant K is used to fill the gap between the plates. Inserting the dielectric changes the energy stored by a factor of

A capacitor consists of a set of two parallel plates of area A separated by a distance d. The capacitor plates carry charges +Q and -Q. If the separation between the plates is doubled, the electrical energy stored in the capacitor will

A parallel-plate capacitor of capacitance C is connected to a battery of voltage V until it is fully charged. The energy density in the capacitor is then equal to u. If the same capacitor is then connected to a battery of voltage 2V its energy density becomes equal to

Capacitance of capacitors depends upon

FIGURE 24-1 -Fig. 24-1 shows 3 capacitors, of equal capacitance C, connected to a battery of voltage V. What is the equivalent capacitance of this combination?

A dielectric material such as paper is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field between the plates?

FIGURE 24-3 -Three capacitors C1, C2, and C3 are connected to a battery as shown in Fig. 24-3. The three capacitors have equal capacitances. Which capacitor stores the most potential energy?

5.00 μF, 10.0 μF, and 50.0 μF capacitors are connected in series across a 12.0-V battery. (a) How much charge is stored in the 5.00-μF capacitor? (b) What is the potential difference across the 10.0-μF capacitor?

A parallel-plate capacitor has plates of area 0.40 m2 and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery. (a) What is the electric field between the plates? (b) What is the capacitance of the capacitor? (c) What is the charge on the capacitor?

When a parallel-plate capacitor of capacitance C is connected to a battery of voltage V, the energy density in the capacitor is u. If the voltage of battery is doubled, which of the following changes would keep the energy density equal to its previous value u?

FIGURE 24-5 -Four capacitors are connected across a 90-V DC source as shown in Fig. 24-5. (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 voltage across the 6-μF capacitor?

If the voltage on a capacitor is doubled, then the energy stored by the capacitor

FIGURE 24-2 -Fig. 24-2 shows three capacitors connected to a battery. The capacitances are such that C1 = 2 C2 and C1 = 3C3. Which capacitor stores the smallest amount of charge?

A 1.0-μF and a 2.0-μF capacitor are connected in series across a 3.0-V battery. (a) What is the voltage across the 1.0-μF capacitor? (b) What is the voltage across the 2.0-μF capacitor?

FIGURE 24-4 -Two parallel-plate capacitors are connected in series to a battery as shown in Fig. 24-4. A dielectric is inserted in capacitor C₁. What happens to the charge on capacitor C₂?

FIGURE 24-3 -Three capacitors C₁, C₂, and C₃ are connected to a battery as shown in Fig. 24-3. The three capacitors have equal capacitances. Which capacitor stores the most potential energy?

A parallel-plate capacitor has plates of area 0.40 m² and plate separation of 0.20 mm. The capacitor is connected to a 9.0 V battery. (a) What is the electric field between the plates? (b) What is the capacitance of the capacitor? (c) What is the charge on the capacitor?

FIGURE 24-2 -Fig. 24-2 shows three capacitors connected to a battery. The capacitances are such that C₁ = 2 C₂ and C₁ = 3C₃. Which capacitor stores the smallest amount of charge?