Q: A computer keyboard uses a capacitor with a dielectric constant $$\kappa = 3.5$$, area $$A = 9.50 \times 10$$^{-5}$$\,\mathrm{m}^2$$, and initial separation $$d = 5.00 \times 10$$^{-3}$$\,\mathrm{m}. $$What is the capacitance before the key is pressed?

$$0.589 \times 10$$^{-12}$$\,\mathrm{F}$$

Q: A $$40\,\mu\mathrm{C}$$ point charge is located in air. What is the electric field at a distance of $$2.0\,\mathrm{cm}$$ from the charge?

$$8.99 \times 10^8$\,\mathrm{V/m}$$

Question 1

Which of the following best describes the electric field between the plates of a parallel plate capacitor (ignoring edge effects)?

Accepted Answer

It is uniform everywhere between the plates.

Question 2

Given a parallel plate capacitor with area $$A$$ and plate separation $$d$$, filled with a dielectric of constant $$\kappa$$, which equation gives the capacitance $$C$$?

Accepted Answer

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

Question 3

A $$10\,\mathrm{F}$$ capacitor is charged to $$3\,\mathrm{V}. $$How much energy is stored in the capacitor?

Accepted Answer

$$45\,\mathrm{J}$$

Question 4

If a dielectric material is inserted between the plates of a capacitor while it is disconnected from a battery (constant charge), what happens to the voltage across the plates?

Accepted Answer

It decreases.

Question 5

Which of the following substances has the highest dielectric constant according to the provided table?

Accepted Answer

Water

Question 6

The energy density $$u$$ stored in the electric field of a capacitor is given by which formula?

Accepted Answer

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

Question 7

A parallel plate capacitor is connected to a battery and a dielectric is inserted. The voltage is kept constant. What happens to the charge on the plates?

Accepted Answer

It increases.

Question 8

What is the SI unit of capacitance?

Accepted Answer

Farad

Question 9

If the separation between the plates of a parallel plate capacitor is halved, what happens to the capacitance?

Accepted Answer

It is doubled.

Question 10

A computer keyboard uses a capacitor with a dielectric constant $$\kappa = 3.5$$, area $$A = 9.50 	imes 10$$^{-5}$$\,\mathrm{m}^2$$, and initial separation $$d = 5.00 	imes 10$$^{-3}$$\,\mathrm{m}. $$What is the capacitance before the key is pressed?

Accepted Answer

$$0.589 	imes 10$$^{-12}$$\,\mathrm{F}$$

Question 11

Which of the following is NOT an advantage of using a dielectric in a capacitor?

Accepted Answer

It increases the likelihood of breakdown (sparking).

Question 12

The dielectric strength of a material is defined as:

Accepted Answer

The maximum electric field a dielectric can withstand without breakdown.

Question 13

If the area of the plates of a parallel plate capacitor is doubled while keeping all other factors constant, what happens to the capacitance?

Accepted Answer

It is doubled.

Question 14

A $$40\,\mu\mathrm{C}$$ point charge is located in air. What is the electric field at a distance of $$2.0\,\mathrm{cm}$$ from the charge?

Accepted Answer

$$8.99 	imes 10^8$\,\mathrm{V/m}$$

Question 15

Which equation correctly relates the electric field $$E$$ and the potential difference $$V$$ for a parallel plate capacitor with plate separation $$d$$?

Accepted Answer

$$E = \frac{V}{d}$$

Question 16

A parallel plate capacitor is charged and then disconnected from the battery. If the plate separation is decreased, what happens to the voltage across the plates?

Accepted Answer

It decreases.

Question 17

Which of the following best explains why the capacitance increases when a dielectric is inserted between the plates of a capacitor?

Accepted Answer

The dielectric reduces the effective electric field, allowing more charge to be stored for the same voltage.

Question 18

If a capacitor stores $$q$$ charge at a potential difference $$V$$, which equation gives the energy stored in the capacitor?

Accepted Answer

$$E = \frac{1}{2} qV$$

Question 19

A parallel plate capacitor is filled with a dielectric of $$\kappa = 3.3$$ and has a plate separation of $$1\,\mu\mathrm{m}. $$What is the effect on the required plate area to achieve $$1\,\mathrm{F}$$ capacitance compared to air?

Accepted Answer

The required area is smaller than in air.

Electric Potential and Capacitance: Parallel Plate Capacitors and Dielectrics

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