Question 1

A parallel-plate capacitor has plates of area $$A$$ separated by a distance $$d in $$vacuum. What is the correct formula for its capacitance $$C$$?

Accepted Answer

$$C = \frac{\$$varepsilon_0$$ A}{d}$$

Question 2

If the charge $$Q on a $$capacitor is doubled while the distance between the plates and the area remain constant, what happens to the potential difference $$V$$ across the plates?

Accepted Answer

It doubles.

Question 3

Two capacitors, $$C_1 = 2$$\ \mu\mathrm{F}$$ and C_2$ = 4\ \mu\mathrm{F}$$, are connected in series. What is their equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$C_{eq} = 1.33\ \mu\mathrm{F}$$

Question 4

A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$100\ \mathrm{V}. $$What is the energy stored in the capacitor?

Accepted Answer

$$0.05\ \mathrm{J}$$

Question 5

A dielectric with dielectric constant $$K is $$inserted between the plates of a charged, isolated parallel-plate capacitor. What happens to the electric field $$E$$ between the plates?

Accepted Answer

It decreases by a factor of $$K.$$

Question 6

Which of the following best describes the effect of adding a dielectric to a capacitor while keeping the voltage across the plates constant?

Accepted Answer

The stored energy increases.

Question 7

A spherical capacitor consists of two concentric spherical shells of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a). $$What is the formula for its capacitance?

Accepted Answer

$$C = 4\pi\$$varepsilon_0$$ \frac{r_a r_b}{r_b - r_a}$$

Question 8

If three capacitors of $$2\ \mu\mathrm{F}$$, $$3\ \mu\mathrm{F}$$, and $$6\ \mu\mathrm{F}$$ are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$$11\ \mu\mathrm{F}$$

Question 9

A capacitor is charged to a voltage $$V_0$$ and then disconnected from the battery. A dielectric is inserted between the plates. What happens to the stored energy?

Accepted Answer

It decreases.

Question 10

Which of the following is a correct statement about the energy density $$u in $$the electric field of a parallel-plate capacitor with a dielectric?

Accepted Answer

$$u = \frac{1}{2} K \$$varepsilon_0$$ E^2$

Question 11

A capacitor network consists of a $$4\ \mu\mathrm{F}$$ and a $$6\ \mu\mathrm{F}$$ capacitor in series, connected in parallel with a $$2\ \mu\mathrm{F}$$ capacitor. What is the equivalent capacitance?

Accepted Answer

$$4\ \mu\mathrm{F}$$

Question 12

A capacitor is connected to a battery and fully charged. The battery is then disconnected, and the distance between the plates is doubled. What happens to the capacitance and the voltage across the plates?

Accepted Answer

Capacitance halves, voltage doubles.

Question 13

Which of the following materials would provide the greatest increase in capacitance when used as a dielectric in a parallel-plate capacitor?

Accepted Answer

Water ($$K = 80.4)$$

Question 14

A capacitor is used in a defibrillator to deliver a quick burst of energy to a patient. If the capacitance is $$100\ \mu\mathrm{F}$$ and the voltage is $$2000\ \mathrm{V}$$, how much energy is delivered?

Accepted Answer

$$200\ \mathrm{J}$$

Question 15

What is the main reason for using a dielectric in a capacitor?

Accepted Answer

To increase the capacitance and allow higher energy storage.

Question 16

A capacitor is charged to $$Q$$ and then disconnected from the battery. If the area of the plates is doubled while the distance remains the same, what happens to the voltage across the plates?

Accepted Answer

It is halved.

Question 17

Which of the following best describes dielectric breakdown?

Accepted Answer

The dielectric becomes a conductor when the electric field exceeds a critical value.

Question 18

A cylindrical capacitor has inner radius $$r_a$$ and outer radius $$r_b$$ and length $$L. $$What is the capacitance per unit length?

Accepted Answer

$$C' = \frac{2\pi\$$varepsilon_0$$}{\ln(r_b/r_a)}$$

Question 19

In a capacitor with a dielectric, what is the relationship between the permittivity $$\varepsilon$$ and the dielectric constant $$K$$?

Accepted Answer

$$\varepsilon = K \$$varepsilon_0$$

Question 20

A capacitor is initially charged and then connected to an uncharged capacitor of equal capacitance. What is the final voltage across both capacitors?

Accepted Answer

Half the initial voltage.

Capacitance and Dielectrics: Principles, Calculations, and Applications

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