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

Accepted Answer

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

Question 9

Which of the following correctly expresses the relationship for capacitors in series?

Accepted Answer

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

Question 10

Two identical capacitors, each of capacitance $C$, are connected in series. What is the equivalent capacitance?

Accepted Answer

$\frac{C}{2}$

Question 11

If a capacitor of $1\ \mathrm{pF}$ is attached in series with a capacitor of $1\ \mathrm{\mu F}$, what is the effective capacitance of the combination?

Accepted Answer

Very close to $1\ \mathrm{pF}$

Question 12

For capacitors in parallel, what is the formula for the equivalent capacitance?

Accepted Answer

$C = C_1 + C_2$

Question 13

If a capacitor of $1\ \mathrm{pF}$ is attached in parallel with a capacitor of $1\ \mathrm{\mu F}$, what is the effective capacitance of the combination?

Accepted Answer

Very close to $1\ \mathrm{\mu F}$

Question 14

When two capacitors are connected in parallel, how does the potential drop across each capacitor compare?

Accepted Answer

The potential drop is the same across each capacitor.

Question 15

What is the energy $U$ stored in a capacitor with charge $Q$ and capacitance $C$?

Accepted Answer

$U = \frac{1}{2} \frac{Q^2}{C}$

Question 16

A parallel-plate capacitor is filled with a dielectric material of dielectric constant $K$. How does the capacitance change?

Accepted Answer

The capacitance increases by a factor of $K$.

Question 17

What is the formula for 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 a dielectric is inserted between the plates of a charged, isolated capacitor, what happens to the voltage across the plates?

Accepted Answer

The voltage decreases.

Capacitors and Capacitance: Principles, Formulas, and Circuit Applications

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