Q: A capacitor is constructed using two parallel plates of area $$2.30\ \mathrm{cm}^2$$ separated by $$1.50\ \mathrm{mm} of $$air. What is the capacitance?

$$1.36 \times 10$$^{-13}$$\ \mathrm{F}$$

Question 1

A parallel-plate capacitor has plates of area $$A$$ separated by a distance $$d in $$vacuum. Which of the following correctly gives the capacitance $$C of $$this capacitor?

Accepted Answer

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

Question 2

A 3.00-$$\muF $$capacitor is connected to a battery and stores a charge of 27.0 $$\muC. $$What is the voltage of the battery?

Accepted Answer

$$9.00\ \mathrm{V}$$

Question 3

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

Accepted Answer

It is stored in the electric field between the plates.

Question 4

A 12-$$\muF $$capacitor and a 6-$$\muF $$capacitor are connected in series. What is their equivalent capacitance?

Accepted Answer

$$4\ \mu\mathrm{F}$$

Question 5

A 12-$$\muF $$capacitor and a 6-$$\muF $$capacitor are connected in parallel. What is their equivalent capacitance?

Accepted Answer

$$18\ \mu\mathrm{F}$$

Question 6

If the charge on a capacitor is kept constant and the capacitance is doubled, what happens to the potential difference across the plates?

Accepted Answer

It becomes half as great.

Question 7

A parallel-plate capacitor with air between the plates is connected to a battery. If a dielectric with dielectric constant $$K is $$inserted between the plates while the battery remains connected, what happens to the charge on the plates?

Accepted Answer

The charge increases by a factor of $$K.$$

Question 8

The energy density $$u$$ stored in the electric field of a parallel-plate capacitor is given by which of the following expressions?

Accepted Answer

$$u = \frac{1}{2} \$$varepsilon_0$$ E^2$

Question 9

A parallel-plate capacitor is charged to a potential $$V$$ and then disconnected from the battery. If a dielectric is inserted between the plates, what happens to the energy stored in the capacitor?

Accepted Answer

The stored energy decreases.

Question 10

A spherical capacitor consists of two concentric spherical conducting shells of radii $$r_a$$ and $$r_b$$ ($$r_b \u003e r_a). $$What is the capacitance of this system?

Accepted Answer

$$C = 4 \pi \$$varepsilon_0$$ \frac{r_a r_b}{r_b - r_a}$$

Question 11

A capacitor is constructed using two parallel plates of area $$2.30\ \mathrm{cm}^2$$ separated by $$1.50\ \mathrm{mm} of $$air. What is the capacitance?

Accepted Answer

$$1.36 	imes 10$$^{-13}$$\ \mathrm{F}$$

Question 12

Which of the following statements about dielectrics is correct?

Accepted Answer

A dielectric increases the capacitance of a capacitor.

Question 13

A parallel-plate capacitor is charged and then disconnected from the battery. If the plate separation is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

The energy is doubled.

Question 14

The dielectric strength of a material is best defined as:

Accepted Answer

The maximum electric field the material can withstand before breakdown.

Question 15

A capacitor is connected to a battery and then a dielectric is inserted while the battery remains connected. What happens to the energy stored in the capacitor?

Accepted Answer

The stored energy increases.

Question 16

Which equation correctly relates the dielectric constant $$K$$, the capacitance with dielectric $$C$$, and the capacitance without dielectric $$C_0$$?

Accepted Answer

$$K = \frac{C}{C_0$}$$

Question 17

A camera’s flash uses a capacitor to store energy. If the capacitor has a capacitance of $$1000\ \mu\mathrm{F}$$ and is charged to $$300\ \mathrm{V}$$, how much energy is stored?

Accepted Answer

$$45\ \mathrm{J}$$

Question 18

A parallel-plate capacitor is charged to a potential $$V$$ and then disconnected from the battery. If the plate separation is halved, what happens to the potential difference across the plates?

Accepted Answer

The potential difference is doubled.

Question 19

Which of the following is a correct expression for the energy stored in a capacitor?

Accepted Answer

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

Question 20

A dielectric material is inserted between the plates of a charged, isolated capacitor. What happens to the electric field between the plates?

Accepted Answer

The electric field decreases.

Capacitance and Dielectrics: Structured Study Notes

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