Q: A capacitor is made from two sheets of aluminum foil separated by waxed paper ($\kappa = 2.50$) of thickness $0.030\ mm$. If the area of each sheet is $0.400\ m \times 0.300\ m$, what is the capacitance?

$8.85 \times 10^{-11}\ F \times 2.50 = 8.85 \times 10^{-11}\ F \times 2.50 = 2.21 \times 10^{-10}\ F$

Question 1

Which of the following correctly describes the behavior of capacitors in parallel?

Accepted Answer

The total capacitance is the sum of the individual capacitances: $C_{eq} = C_1 + C_2 + ... + C_n$

Question 2

A parallel plate capacitor has plates of area $A$ separated by distance $d$. What is the capacitance if the space between the plates is filled with a dielectric of constant $\kappa$?

Accepted Answer

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

Question 3

Three capacitors, each of $12.0\ \mu F$, are arranged such that $C_2$ and $C_3$ are in parallel and their combination is in series with $C_1$. What is the equivalent capacitance?

Accepted Answer

$8.00\ \mu F$

Question 4

If a capacitor is connected to a battery and then a dielectric is inserted between its plates, what happens to the charge $Q$ and voltage $V$ across the capacitor?

Accepted Answer

$V$ stays the same, $Q$ increases

Question 5

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

Accepted Answer

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

Question 6

A parallel plate capacitor with air gap has plates of $0.400\ m 	imes 0.300\ m$ separated by $0.030\ mm$. What is the capacitance?

Accepted Answer

$3.54 	imes 10^{-11}\ F$

Question 7

Which statement about capacitors in series is correct?

Accepted Answer

The charge on each capacitor is the same

Question 8

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 9

A capacitor is made from two sheets of aluminum foil separated by waxed paper ($\kappa = 2.50$) of thickness $0.030\ mm$. If the area of each sheet is $0.400\ m 	imes 0.300\ m$, what is the capacitance?

Accepted Answer

$8.85 	imes 10^{-11}\ F 	imes 2.50 = 8.85 	imes 10^{-11}\ F 	imes 2.50 = 2.21 	imes 10^{-10}\ F$

Question 10

If the battery is disconnected before inserting a dielectric between the plates of a charged capacitor, what happens?

Accepted Answer

The charge $Q$ remains the same, but the voltage $V$ decreases

Question 11

Which of the following best describes the effect of inserting a dielectric into a capacitor?

Accepted Answer

It increases the capacitance by a factor equal to the dielectric constant $\kappa$

Question 12

A parallel plate capacitor is charged to a potential difference $V$ and then disconnected from the battery. A dielectric slab is inserted between the plates. What happens to the energy stored in the capacitor?

Accepted Answer

The energy decreases

Question 13

What is the unit of capacitance?

Accepted Answer

Farad ($F$)

Question 14

Which formula gives the potential difference $\Delta V$ between the plates of a capacitor in terms of the electric field $E$?

Accepted Answer

$\Delta V = - \int_a^b \vec{E} \cdot d\vec{l}$

Question 15

Which of the following is true for polar dielectrics placed in an external electric field?

Accepted Answer

Molecular dipoles align with the external field, creating an internal field opposing the external field

Question 16

A cylindrical capacitor has inner radius $R_1$, outer radius $R_2$, and length $L$. What is its capacitance?

Accepted Answer

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

Question 17

What is dielectric breakdown?

Accepted Answer

The point at which the electric field in a dielectric becomes strong enough to allow charge to flow through the material

Question 18

Which of the following is the correct expression for the energy stored in a capacitor in terms of capacitance $C$ and voltage $V$?

Accepted Answer

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

Question 19

If two capacitors $C_1$ and $C_2$ are connected in series, what is the equivalent capacitance?

Accepted Answer

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

Capacitance and Dielectrics: Principles, Circuits, and Applications

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