Question 1

A parallel plate capacitor has plates of area $A$ separated by a distance $d$ in vacuum. What is the correct formula for its capacitance?

Accepted Answer

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

Question 2

Which of the following changes will increase the capacitance of a parallel plate capacitor, all else being equal?

Accepted Answer

Inserting a dielectric with $K > 1$ between the plates

Question 3

A capacitor is charged to a potential $V$ and then disconnected from the battery. If the plate separation is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

It increases by a factor of 2

Question 4

For a spherical capacitor with inner radius $r_a$ and outer radius $r_b$, what is the correct expression for its capacitance?

Accepted Answer

$C = 4\pi \epsilon_0 \frac{r_a r_b}{r_b - r_a}$

Question 5

Three capacitors, $C_1$, $C_2$, and $C_3$, are connected in series. Which of the following statements is true?

Accepted Answer

The charge on each capacitor is the same

Question 6

A parallel plate capacitor is filled with a dielectric of constant $K$. What is the new capacitance compared to the original capacitance $C_0$ (without dielectric)?

Accepted Answer

$C = K C_0$

Question 7

A capacitor is connected to a battery and a dielectric is inserted between its plates. Which of the following quantities remains unchanged?

Accepted Answer

The potential difference across the plates

Question 8

The energy stored in a capacitor is given by which of the following expressions?

Accepted Answer

$U = \frac{1}{2} QV$

Question 9

A cylindrical capacitor consists of two coaxial cylinders of length $L$, inner radius $r_a$, and outer radius $r_b$. What is the capacitance per unit length?

Accepted Answer

$C' = \frac{2\pi \epsilon_0}{\ln(r_b/r_a)}$

Question 10

A parallel plate capacitor with area $A$ and separation $d$ is charged to $Q$ and then disconnected from the battery. If a dielectric with constant $K$ is inserted, what happens to the potential difference across the plates?

Accepted Answer

It decreases by a factor of $K$

Question 11

Which of the following best describes the energy density $u$ of the electric field in a parallel plate capacitor?

Accepted Answer

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

Question 12

A capacitor network consists of a $7.5$ nF and $6.5$ nF capacitor in parallel, each in series with a combination of $18.0$ nF, $30.0$ nF, and $10.0$ nF capacitors. If the total voltage is $25$ V, what is the total charge stored in the network?

Accepted Answer

$482$ nC

Question 13

Which of the following statements about the effect of a dielectric on a capacitor is correct?

Accepted Answer

The dielectric increases the capacitance and decreases the electric field for a given charge

Question 14

A parallel plate capacitor has a metal sheet of thickness $b$ inserted between its plates (separation $d$). How can the new capacitance be calculated?

Accepted Answer

By treating it as two capacitors in series: one with separation $b$ and one with separation $d-b$

Question 15

Which of the following is NOT a practical application of capacitors?

Accepted Answer

Measuring temperature in thermocouples

Question 16

If a parallel plate capacitor is connected to a battery and the plate separation is increased, what happens to the charge on the plates?

Accepted Answer

It decreases

Question 17

The capacitance of the Earth, modeled as an isolated conducting sphere of radius $R$, is given by:

Accepted Answer

$C = 4\pi \epsilon_0 R$

Question 18

Which of the following best describes the relationship between free and bound charge in a capacitor with a dielectric?

Accepted Answer

Free charge is on the plates, bound charge is induced on the dielectric surfaces

Question 19

A capacitor is made of two parallel plates of area $A$ and separation $d$, filled with a dielectric of constant $K$. What is the correct expression for its capacitance?

Accepted Answer

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

Capacitance and Capacitors: Principles, Types, and Applications

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