Q: A capacitor is charged to a potential difference of $$120\ \text{V}$$ and has a capacitance of $$25\ \mu\text{F}. $$How much charge is stored?

$$q = (25 \times 10$$^{-6}$$\ \text{F})(120\ \text{V}) = 3.0 \times 10$$^{-3}$$\ \text{C}$$

Question 1

A parallel-plate capacitor has plates of area $$A$$ separated by distance $$d. If $$the space between the plates is filled with a dielectric material of dielectric constant $$\kappa$$, what is the new capacitance?

Accepted Answer

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

Question 2

Which of the following correctly describes the energy stored in a capacitor with capacitance $$C$$ and potential difference $$V$$?

Accepted Answer

$$U = \frac{1}{2} CV^2$

Question 3

A spherical capacitor consists of two concentric spheres with radii $$a$$ and $$b$$ ($$b \u003e a). $$What is the formula for its capacitance?

Accepted Answer

$$C = 4\pi \$$epsilon_0$$ \frac{ab}{b-a}$$

Question 4

Three capacitors with capacitances $$C_1$$, $$C_2$$, and $$C_3$$ are connected in series. What is the equivalent capacitance?

Accepted Answer

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

Question 5

A parallel-plate capacitor has plates of radius $$r = 8.2\ 	ext{cm}$$ and separation $$d = 1.3\ 	ext{mm}. $$What is the capacitance?

Accepted Answer

$$C = \$$epsilon_0$$ \frac{\pi r^2$}{d}$$

Question 6

If a capacitor is charged to a potential difference $$V$$ and then disconnected from the battery, what happens to the charge on the plates if a dielectric is inserted between them?

Accepted Answer

The charge remains the same.

Question 7

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

Accepted Answer

$$C = 2\pi \$$epsilon_0$$ \frac{L}{\ln(b/a)}$$

Question 8

A capacitor with capacitance $$C is $$connected to a battery of voltage $$V. $$How much charge $$q is $$stored on the plates?

Accepted Answer

$$q = CV$$

Question 9

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

Accepted Answer

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

Question 10

You have two flat metal plates, each of area $$1.00\ 	ext{m}^2$$, and want to construct a parallel-plate capacitor with capacitance $$1.00\ 	ext{F}. $$What must be the separation $$d$$ between the plates?

Accepted Answer

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

Question 11

Three capacitors $$C_1 = 10.0$$\ \mu	ext{F}$$, C_2$ = 5.00\ \mu	ext{F}$$, and $$C_3 = 4.00$$\ \mu	ext{F}$$ are arranged so that C_1$ and C_2$ are in series, and their combination is in parallel with C_3$. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = \left(\frac{1}{C_1$} + \frac{1}{C_2$}\$$right)^{-1}$$ + C_3$

Question 12

A capacitor is charged to a potential difference of $$120\ 	ext{V}$$ and has a capacitance of $$25\ \mu	ext{F}. $$How much charge is stored?

Accepted Answer

$$q = (25 	imes 10$$^{-6}$$\ 	ext{F})(120\ 	ext{V}) = 3.0 	imes 10$$^{-3}$$\ 	ext{C}$$

Question 13

If $$n$$ identical capacitors of capacitance $$C$$ are connected in parallel across a voltage $$V$$, what is the total charge $$q_{tot}$$ stored?

Accepted Answer

$$q_{tot} = nCV$$

Question 14

A spherical capacitor has inner radius $$a$$ and outer radius $$b = 2a. If $$its capacitance is $$2.0\ \mu	ext{F}$$, what is the value of $$a$$?

Accepted Answer

$$a = \frac{C}{8\pi \$$epsilon_0$$}$$

Question 15

Which statement about capacitors in parallel is correct?

Accepted Answer

The equivalent capacitance is the sum of the individual capacitances.

Question 16

A capacitor is filled with a dielectric material. Which of the following is true about the dielectric constant $$\kappa$$?

Accepted Answer

$$\kappa is $$unitless and always greater than 1 for real materials.

Question 17

If the energy stored in a capacitor is $$U = \frac{1}{2} CV^2$, what happens to the energy if the voltage is doubled?

Accepted Answer

The energy increases by a factor of 4.

Question 18

Which of the following is the correct SI unit for capacitance?

Accepted Answer

Farad ($$	ext{F})$$

Question 19

A parallel-plate capacitor is constructed with plates of area $$A$$ and separation $$d. If $$the separation is halved, what happens to the capacitance?

Accepted Answer

The capacitance doubles.

Capacitance and Dielectrics: Concepts, Calculations, and Applications

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