Q: A $10.0\ \mu\mathrm{F}$ and a $20.0\ \mu\mathrm{F}$ capacitor are connected in parallel across a $12.0\ \mathrm{V}$ battery. What is the total energy stored in the system?

$2.16 \times 10^{-3}\ \mathrm{J}$

Q: A parallel-plate capacitor has a plate area of $0.02\ \mathrm{m}^2$ and a separation of $1.0\ \mathrm{mm}$. What is its capacitance in air? ($\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F/m}$)

$1.77 \times 10^{-10}\ \mathrm{F}$

Q: A capacitor is constructed from two sheets of aluminum foil, each $0.300\ \mathrm{m} \times 0.400\ \mathrm{m}$, separated by a $0.030\ \mathrm{mm}$ thick waxed paper with $\kappa = 2.5$. What is the capacitance? ($\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F/m}$)

$8.85 \times 10^{-9}\ \mathrm{F}$

Question 1

A parallel-plate capacitor has plates of area $A$ separated by a distance $d$ and is filled with air. If a dielectric with dielectric constant $\kappa$ is inserted fully between the plates while the capacitor is disconnected from any battery, what happens to the voltage across the plates?

Accepted Answer

The voltage decreases by a factor of $\kappa$.

Question 2

Which of the following correctly expresses the equivalent capacitance $C_{eq}$ for three capacitors $C_1$, $C_2$, and $C_3$ connected in series?

Accepted Answer

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

Question 3

A $10.0\ \mu\mathrm{F}$ and a $20.0\ \mu\mathrm{F}$ capacitor are connected in parallel across a $12.0\ \mathrm{V}$ battery. What is the total energy stored in the system?

Accepted Answer

$2.16 	imes 10^{-3}\ \mathrm{J}$

Question 4

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

Accepted Answer

The charge on each capacitor is the same.

Question 5

A parallel-plate capacitor with plate area $A$ and separation $d$ is connected to a battery of voltage $V$. If the plate separation is doubled while the battery remains connected, what happens to the energy stored in the capacitor?

Accepted Answer

It decreases by a factor of 2.

Question 6

The energy density $u$ stored in the electric field of a parallel-plate capacitor is given by which of the following expressions?

Accepted Answer

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

Question 7

A capacitor is made from two concentric cylinders of length $L$, with radii $R_1$ and $R_2$ ($R_2 > R_1$). What is the capacitance of this cylindrical capacitor?

Accepted Answer

$C = \dfrac{2 \pi \varepsilon_0 L}{\ln(\frac{R_2}{R_1})}$

Question 8

A $5.0\ \mu\mathrm{F}$ capacitor is charged to $100\ \mathrm{V}$ and then disconnected from the battery. If a dielectric with $\kappa = 4$ is inserted, what is the new voltage across the capacitor?

Accepted Answer

$25\ \mathrm{V}$

Question 9

Which of the following best describes the effect of inserting a dielectric into a capacitor while it is still connected to a battery?

Accepted Answer

The capacitance and stored charge increase, but the voltage remains constant.

Question 10

A parallel-plate capacitor has a plate area of $0.02\ \mathrm{m}^2$ and a separation of $1.0\ \mathrm{mm}$. What is its capacitance in air? ($\varepsilon_0 = 8.85 	imes 10^{-12}\ \mathrm{F/m}$)

Accepted Answer

$1.77 	imes 10^{-10}\ \mathrm{F}$

Question 11

A capacitor is constructed from two sheets of aluminum foil, each $0.300\ \mathrm{m} 	imes 0.400\ \mathrm{m}$, separated by a $0.030\ \mathrm{mm}$ thick waxed paper with $\kappa = 2.5$. What is the capacitance? ($\varepsilon_0 = 8.85 	imes 10^{-12}\ \mathrm{F/m}$)

Accepted Answer

$8.85 	imes 10^{-9}\ \mathrm{F}$

Question 12

Which of the following is true about the dielectric strength of a material?

Accepted Answer

It is the maximum electric field the material can withstand before breakdown.

Question 13

A $12.0\ \mu\mathrm{F}$ and a $24.0\ \mu\mathrm{F}$ capacitor are connected in series. What is their equivalent capacitance?

Accepted Answer

$8.0\ \mu\mathrm{F}$

Question 14

Which of the following best describes a polar dielectric?

Accepted Answer

It consists of molecules with permanent electric dipole moments.

Question 15

If the energy stored in a capacitor is $U = \dfrac{1}{2} C V^2$, what happens to the stored energy if the voltage is doubled while the capacitance remains constant?

Accepted Answer

The energy increases by a factor of 4.

Question 16

A parallel-plate capacitor is connected to a $150\ \mathrm{V}$ battery and has a plate area of $0.01\ \mathrm{m}^2$ and separation $0.75\ \mathrm{mm}$. What is the charge stored on the capacitor? ($\varepsilon_0 = 8.85 	imes 10^{-12}\ \mathrm{F/m}$)

Accepted Answer

$1.77 	imes 10^{-9}\ \mathrm{C}$

Question 17

Which of the following is the correct unit for capacitance?

Accepted Answer

$\mathrm{C/V}$

Question 18

A parallel-plate capacitor is filled halfway with a dielectric of constant $\kappa$ and the other half with air. How does the total capacitance compare to the original air-filled capacitor?

Accepted Answer

It is greater than the original capacitance but less than if the entire space were filled with the dielectric.

Question 19

Which of the following best describes the energy stored in a capacitor in terms of charge $Q$ and capacitance $C$?

Accepted Answer

$U = \dfrac{Q^2}{2C}$

Capacitance and Dielectrics: Principles, Circuits, and Applications

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