Q: Which of the following is the correct value for the permittivity of free space $\epsilon_0$?

$8.854 \times 10^{-12} \ \dfrac{C^2}{N m^2}$

Question 1

A parallel-plate capacitor consists of two metal plates of area $A$ separated by a distance $d$. If the plates carry charges $+Q$ and $-Q$, what is the magnitude of the electric field between the plates (assuming vacuum between them)?

Accepted Answer

$E = \dfrac{Q}{\epsilon_0 A}$

Question 2

Which of the following correctly expresses the capacitance $C$ of a parallel-plate capacitor with plate area $A$ and separation $d$ (in vacuum)?

Accepted Answer

$C = \dfrac{\epsilon_0 A}{d}$

Question 3

A parallel-plate capacitor is connected to a battery that maintains a constant potential difference $V$. If the plates are moved closer together, what happens to the charge on each plate?

Accepted Answer

The charge on each plate increases.

Question 4

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

Accepted Answer

The potential difference increases.

Question 5

Two capacitors, $C_1$ and $C_2$, are connected in series. Which formula gives the equivalent capacitance $C$?

Accepted Answer

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

Question 6

Two capacitors, $C_1$ and $C_2$, are connected in parallel. Which formula gives the equivalent capacitance $C$?

Accepted Answer

$C = C_1 + C_2$

Question 7

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

Accepted Answer

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

Question 8

A parallel-plate capacitor with area $A$ and separation $d$ is filled with a dielectric of constant $K$. What is the new capacitance?

Accepted Answer

$C = K \dfrac{\epsilon_0 A}{d}$

Question 9

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.

Question 10

Which of the following is the correct value for the permittivity of free space $\epsilon_0$?

Accepted Answer

$8.854 	imes 10^{-12} \ \dfrac{C^2}{N m^2}$

Question 11

A $10\ \mu F$ and a $20\ \mu F$ capacitor are connected in series across a $30\ V$ battery. What is the equivalent capacitance?

Accepted Answer

$\dfrac{1}{C} = \dfrac{1}{10} + \dfrac{1}{20}$, so $C = 6.67\ \mu F$

Question 12

A $10\ \mu F$ and a $20\ \mu F$ capacitor are connected in parallel across a $30\ V$ battery. What is the equivalent capacitance?

Accepted Answer

$C = 30\ \mu F$

Question 13

A parallel-plate capacitor is connected to a battery and then disconnected. If the plate separation is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

The energy increases.

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

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

Accepted Answer

$u = \dfrac{1}{2} \epsilon_0 E^2$

Question 17

A parallel-plate capacitor is filled with a dielectric material. For a fixed charge, what can be said about the dielectric constant $K$?

Accepted Answer

$K$ is greater than 1.

Question 18

If a capacitor is connected to a battery and a dielectric is inserted between the plates, what happens to the charge on the plates?

Accepted Answer

The charge increases.

Question 19

Which of the following is the correct expression for Coulomb's constant $k$ in terms of $\epsilon_0$?

Accepted Answer

$k = \dfrac{1}{4 \pi \epsilon_0}$

Capacitors and Capacitance: Principles, Formulas, and Circuit Applications

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