Question 1

Which of the following best describes the physical meaning of capacitance for a parallel-plate capacitor?

Accepted Answer

The ratio of the charge stored on the plates to the electric potential difference between them.

Question 2

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

Accepted Answer

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

Question 3

If the potential difference across a capacitor is doubled while keeping the capacitance constant, what happens to the energy stored in the capacitor?

Accepted Answer

It increases by a factor of four.

Question 4

Which of the following is the correct expression for the energy stored in a charged capacitor?

Accepted Answer

$$U = \frac{1}{2} C (\Delta V)^2$

Question 5

A dielectric material with dielectric constant $$k is $$inserted between the plates of a parallel-plate capacitor. What happens to the capacitance?

Accepted Answer

It increases by a factor of $$k.$$

Question 6

For three capacitors $$C_1$$, $$C_2$$, and $$C_3$$ connected in series, which equation correctly relates their equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$\frac{1}{C_{eq}} = \frac{1}{C_1$} + \frac{1}{C_2$} + \frac{1}{C_3$}$$

Question 7

A cylindrical capacitor consists of a solid cylindrical conductor of radius $$a$$ and a coaxial cylindrical shell of radius $$b \u003e a. $$What is the formula for its capacitance per unit length?

Accepted Answer

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

Question 8

Which of the following statements about the effect of a dielectric on a capacitor is correct?

Accepted Answer

The dielectric increases the capacitance and allows for a higher maximum operating voltage.

Question 9

The dielectric constant $$k is $$defined as:

Accepted Answer

$$k = \frac{E_0$}{E}$$

Question 10

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

Accepted Answer

$$C = 4 \pi \$$varepsilon_0$$ \frac{ab}{b-a}$$

Question 11

If a capacitor is charged and then disconnected from the battery, what happens to the charge and voltage across the plates if a dielectric is inserted?

Accepted Answer

The charge remains constant and the voltage decreases.

Question 12

Which of the following is the correct SI unit for capacitance?

Accepted Answer

Farad (F)

Question 13

The permittivity of a dielectric material $$\varepsilon is $$related to the permittivity of free space $$\$$varepsilon_0$$ and the dielectric constant k$ by:

Accepted Answer

$$\varepsilon = k \$$varepsilon_0$$

Question 14

A capacitor is connected to a battery and a dielectric is inserted between its plates. Which of the following statements is true?

Accepted Answer

The charge on the capacitor increases while the voltage remains constant.

Question 15

Which of the following best explains why inserting a dielectric increases the maximum operating voltage of a capacitor?

Accepted Answer

The dielectric increases the breakdown electric field strength.

Question 16

If the area of the plates of a parallel-plate capacitor is doubled while the separation is halved, how does the capacitance change?

Accepted Answer

It increases by a factor of 4.

Question 17

Which of the following is NOT a correct way to express the energy stored in a capacitor?

Accepted Answer

$$U = Q C \Delta V$$

Question 18

A parallel-plate capacitor is charged to a voltage $$\Delta V$$ and then disconnected from the battery. If the separation between the plates is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

It decreases by a factor of 2.

Capacitance and Dielectrics: Study Notes for College Physics

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