Question 1

A parallel-plate capacitor has plates of area $$A$$ separated by a distance $$d. If $$the plates are connected to a battery of voltage $$V$$, what is the expression for the capacitance of the capacitor in terms of the permittivity of free space $$\$$varepsilon_0$$?

Accepted Answer

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

Question 2

Which of the following statements about capacitors in series is correct?

Accepted Answer

The equivalent capacitance is always less than any individual capacitor in the series.

Question 3

A capacitor is charged to a voltage $$V_0$$ and then disconnected from the battery. A dielectric with dielectric constant $$\kappa is $$inserted between the plates. What happens to the potential difference across the plates?

Accepted Answer

It decreases by a factor of $$\kappa.$$

Question 4

What is the energy stored in a capacitor with capacitance $$C$$ and voltage $$V$$?

Accepted Answer

$$U = \frac{1}{2}CV^2$

Question 5

A spherical capacitor consists of two concentric spheres of radii $$a$$ and $$b$$ ($$b \u003e a). $$What is the expression for its capacitance?

Accepted Answer

$$C = 4\pi \$$varepsilon_0$$ ab/(b-a)$$

Question 6

Which of the following materials would most likely be used as a dielectric in a capacitor?

Accepted Answer

Glass

Question 7

If two capacitors $$C_1$$ and $$C_2$$ are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$$C_{eq} = C_1$ + C_2$

Question 8

A capacitor is used in a defibrillator to deliver a quick pulse of energy to the heart. If the capacitor stores a charge $$Q at $$voltage $$V$$, what is the total energy delivered?

Accepted Answer

$$U = \frac{1}{2}QV$$

Question 9

What is the effect of inserting a dielectric with dielectric constant $$\kappa$$ into a parallel-plate capacitor?

Accepted Answer

The capacitance increases by a factor of $$\kappa.$$

Question 10

Which equation correctly describes the energy density $$u_E in $$the electric field of a parallel-plate capacitor with dielectric constant $$\kappa$$?

Accepted Answer

$$u_E = \frac{1}{2}\kappa \$$varepsilon_0$$ E^2$

Question 11

A cylindrical capacitor consists of two coaxial cylinders of length $$l$$, radii $$a$$ and $$b$$ ($$b \u003e a). $$What is the expression for its capacitance?

Accepted Answer

$$C = \frac{2\pi \$$varepsilon_0$$ l}{\ln(b/a)}$$

Question 12

Which of the following best describes the role of a dielectric in a capacitor?

Accepted Answer

It increases the capacitance and allows higher operating voltage.

Question 13

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If the plate separation is doubled, what happens to the stored energy?

Accepted Answer

The stored energy increases by a factor of two.

Question 14

Which of the following is NOT a typical application of capacitors?

Accepted Answer

Generating electrical energy in power plants

Question 15

What is the SI unit of capacitance?

Accepted Answer

Farad (F)

Question 16

Which formula gives the surface charge density $$\sigma on $$the plates of a parallel-plate capacitor?

Accepted Answer

$$\sigma = Q/A$$

Question 17

A capacitor is connected to a battery and reaches equilibrium. What is true about the potential difference across the plates?

Accepted Answer

It is equal to the battery voltage.

Question 18

Which of the following statements about polar molecules is correct?

Accepted Answer

They have a permanent separation between positive and negative charge centers.

Question 19

What is the maximum electric field that can exist in a dielectric before breakdown occurs called?

Accepted Answer

Dielectric strength

Question 20

If a capacitor is filled with a dielectric and the dielectric constant is $$\kappa$$, what happens to the electric field between the plates?

Accepted Answer

It decreases by a factor of $$\kappa.$$

Capacitance and Dielectrics: Principles, Calculations, and Applications

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