Q: What is the value and unit of the vacuum permittivity $$\$$varepsilon_0$$?

$$\$$varepsilon_0$$ = 8.854 \times 10$$^{-12}$$ \ \mathrm{C}^2/\mathrm{N} \cdot \mathrm{m}^2$$

Question 1

Which equation correctly defines the capacitance $$C of a $$capacitor in terms of the charge $$Q$$ and the potential difference $$V_{ab}$$ between its plates?

Accepted Answer

$$C = \frac{Q}{V_{ab}}$$

Question 2

For a parallel-plate capacitor with plate area $$A$$ and separation $$d$$, what is the formula for its capacitance in vacuum?

Accepted Answer

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

Question 3

What is the value and unit of the vacuum permittivity $$\$$varepsilon_0$$?

Accepted Answer

$$\$$varepsilon_0$$ = 8.854 	imes 10$$^{-12}$$ \ \mathrm{C}^2/\mathrm{N} \cdot \mathrm{m}^2$$

Question 4

If the separation $$d$$ between the plates of a parallel-plate capacitor is doubled while keeping the plate area $$A$$ constant, what happens to the capacitance?

Accepted Answer

The capacitance is halved.

Question 5

A parallel-plate capacitor is held at a fixed potential difference. If the plates are moved closer together, what happens to the charge on each plate?

Accepted Answer

The charge on each plate increases.

Question 6

A parallel-plate capacitor is charged to a potential difference $$V$$ and then disconnected from the battery. If the plates are moved closer together, what happens to the charge on each plate?

Accepted Answer

The charge on each plate stays the same.

Question 7

A parallel-plate capacitor is charged to a potential difference $$V$$ and then disconnected from the battery. If the plates are moved closer together, what happens to the potential difference between the plates?

Accepted Answer

The potential difference decreases.

Question 8

What is the correct formula for the electric field $$E$$ between the plates of a parallel-plate capacitor?

Accepted Answer

$$E = \frac{Q}{\$$varepsilon_0$$ A}$$

Question 9

Two capacitors, $$C_1$$ and $$C_2$$, are connected in series. What is the correct formula for their equivalent capacitance $$C$$?

Accepted Answer

$$\frac{1}{C} = \frac{1}{C_1$} + \frac{1}{C_2$}$$

Question 10

Two capacitors, $$C_1$$ and $$C_2$$, are connected in parallel. What is the correct formula for their equivalent capacitance $$C$$?

Accepted Answer

$$C = C_1$ + C_2$

Question 11

A capacitor is charged to a charge $$Q$$ and potential $$V. $$What is the energy $$U$$ stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2} Q V$$

Question 12

If a dielectric material with dielectric constant $$K is $$inserted between the plates of a capacitor, how does the capacitance change?

Accepted Answer

The capacitance increases by a factor of $$K.$$

Question 13

A capacitor with capacitance $$C is $$connected to a battery of voltage $$V. If $$the battery is removed and a dielectric is inserted, what happens to the voltage across the capacitor?

Accepted Answer

The voltage decreases.

Question 14

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

Accepted Answer

The charge on each capacitor is the same.

Question 15

Which of the following statements about capacitors in parallel is TRUE?

Accepted Answer

The potential difference across each capacitor is the same.

Question 16

A parallel-plate capacitor is filled with a dielectric of constant $$K. $$What is the new capacitance $$C' in $$terms of the original capacitance $$C$$?

Accepted Answer

$$C' = K C$$

Question 17

What is the energy density $$u$$ stored in the electric field between the plates of a parallel-plate capacitor?

Accepted Answer

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

Question 18

If two identical capacitors, each of capacitance $$C$$, are connected in series, what is the equivalent capacitance?

Accepted Answer

$$\frac{C}{2}$$

Question 19

If two identical capacitors, each of capacitance $$C$$, are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$$2C$$

Capacitors and Capacitance: Principles, Formulas, and Circuit Applications

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