Question 1

Which of the following best defines the capacitance $C$ of a parallel-plate capacitor?

Accepted Answer

$C = \dfrac{Q}{V}$, where $Q$ is the charge stored and $V$ is the potential difference across the plates.

Question 2

A parallel-plate capacitor has plates of area $A$ separated by a distance $d$ and filled with a dielectric of permittivity $\varepsilon$. What is the formula for its capacitance?

Accepted Answer

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

Question 3

Which of the following correctly describes the equivalent capacitance $C_{eq}$ for two capacitors $C_1$ and $C_2$ connected in series?

Accepted Answer

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

Question 4

If three capacitors $C_1$, $C_2$, and $C_3$ are connected in parallel, what is the total capacitance $C_{eq}$?

Accepted Answer

$C_{eq} = C_1 + C_2 + C_3$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is the correct expression for the energy density $u$ stored in the electric field between the plates of a parallel-plate capacitor?

Accepted Answer

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

Question 7

A cylindrical capacitor consists of two coaxial cylinders of length $L$, inner radius $a$, and outer radius $b$. What is its capacitance?

Accepted Answer

$C = \dfrac{2 \pi \varepsilon L}{\ln(b/a)}$

Question 8

In a circuit, a $4\,\mu\mathrm{F}$ and a $6\,\mu\mathrm{F}$ capacitor are connected in series. What is the equivalent capacitance?

Accepted Answer

$C_{eq} = 2.4\,\mu\mathrm{F}$

Question 9

Which statement is true about the voltage across capacitors connected in parallel?

Accepted Answer

All capacitors in parallel have the same voltage across their plates.

Question 10

A $10\,\mu\mathrm{F}$ capacitor is charged to $100\,\mathrm{V}$. How much energy is stored in the capacitor?

Accepted Answer

$U = 0.05\,\mathrm{J}$

Question 11

Which of the following is NOT a standard circuit symbol for a capacitor?

Accepted Answer

A zigzag line

Question 12

If a $5\,\mu\mathrm{F}$ and a $10\,\mu\mathrm{F}$ capacitor are connected in parallel, what is the equivalent capacitance?

Accepted Answer

$C_{eq} = 15\,\mu\mathrm{F}$

Question 13

A capacitor is connected to a battery and reaches a steady state. Which of the following statements is true?

Accepted Answer

The charge on the capacitor is proportional to the voltage of the battery.

Question 14

Which physical quantity does the capacitance of a capacitor NOT depend on?

Accepted Answer

The charge stored on the plates

Question 15

A $2\,\mu\mathrm{F}$, $3\,\mu\mathrm{F}$, and $6\,\mu\mathrm{F}$ capacitor are connected in series. What is the equivalent capacitance?

Accepted Answer

$C_{eq} = 1\,\mu\mathrm{F}$

Question 16

Which of the following is a real-world application of capacitors?

Accepted Answer

Storing energy in camera flashes

Question 17

A $12\,\mu\mathrm{F}$ capacitor and a $6\,\mu\mathrm{F}$ capacitor are connected in series. What is the equivalent capacitance?

Accepted Answer

$C_{eq} = 4\,\mu\mathrm{F}$

Question 18

Which of the following statements about energy storage in a capacitor is correct?

Accepted Answer

The energy stored increases with the square of the voltage.

Question 19

A $5\,\mu\mathrm{F}$ and a $10\,\mu\mathrm{F}$ capacitor are connected in series across a $100\,\mathrm{V}$ battery. What is the charge on each capacitor?

Accepted Answer

$Q = 333\,\mu\mathrm{C}$

Question 20

Which of the following is true for capacitors in series?

Accepted Answer

The charge on each capacitor is the same.

Capacitance and Capacitor Circuits: Study Notes for PHY 131

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