Question 1

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

Accepted Answer

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

Question 2

Which of the following best describes the energy stored in a capacitor?

Accepted Answer

It is stored as electric potential energy in the electric field between the plates.

Question 3

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

Accepted Answer

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

Question 4

A $$3\,\mu	ext{F}$$ and an $$11\,\mu	ext{F}$$ capacitor are connected in parallel. What is their equivalent capacitance?

Accepted Answer

$$C_{eq} = 14\,\mu	ext{F}$$

Question 5

A parallel-plate capacitor is charged to a voltage $$V_0$$ and then disconnected from the battery. A dielectric with dielectric constant $$K is $$inserted between the plates. What happens to the voltage across the plates?

Accepted Answer

It decreases to $$V_0/K$.

Question 6

Which of the following is NOT a reason for using a dielectric in a capacitor?

Accepted Answer

To decrease the permittivity of the material.

Question 7

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

Accepted Answer

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

Question 8

A $$8.0\,\mu	ext{F}$$ capacitor is charged to $$120\,	ext{V}. $$What is the charge stored on the capacitor?

Accepted Answer

$$Q = 960\,\mu	ext{C}$$

Question 9

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

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

Question 10

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

Accepted Answer

The equivalent capacitance is less than the smallest individual capacitance.

Question 11

A camera flash uses a capacitor to store energy. If the capacitor is charged to $$V$$ and has capacitance $$C$$, what is the energy released in the flash?

Accepted Answer

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

Question 12

A dielectric is inserted into a charged capacitor that is disconnected from the battery. Which of the following quantities remains unchanged?

Accepted Answer

The charge on the plates.

Question 13

The dielectric strength of a material is best defined as:

Accepted Answer

The maximum electric field the material can withstand before breakdown.

Question 14

A parallel-plate capacitor is connected to a battery and then a dielectric is inserted while still connected. What happens to the charge on the plates?

Accepted Answer

It increases.

Question 15

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

Accepted Answer

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

Question 16

A $$2000\,	ext{cm}^2$$ parallel-plate capacitor is charged to $$3.00\,	ext{kV}$$ and then disconnected. A dielectric is inserted, reducing the voltage to $$1.00\,	ext{kV}. $$What is the dielectric constant $$K$$?

Accepted Answer

$$K = 3.0$$

Question 17

Which of the following is a real-world application of capacitors that relies on their ability to store and quickly release energy?

Accepted Answer

Camera flash

Question 18

If the electric field in a dielectric-filled capacitor is $$E_0$$ without the dielectric and $$E$$ with the dielectric, what is the relationship between them?

Accepted Answer

$$E = E_0$/K$$

Question 19

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

Accepted Answer

$$C = \dfrac{2 \pi \$$epsilon_0$$ L}{\ln(r_b/r_a)}$$

Capacitance and Dielectrics: Fundamentals, Networks, and Applications

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