Q: A parallel-plate capacitor is connected to a 12 V battery and has a capacitance of $$4\ \mu\mathrm{F}. $$How much energy is stored in the capacitor?

$$2.88 \times 10$$^{-4}$$\ \mathrm{J}$$

Q: A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$100\ \mathrm{V}. $$How much charge is stored on the capacitor?

$$1.0 \times 10$$^{-3}$$\ \mathrm{C}$$

Q: A capacitor is constructed with plates of area $$0.02\ \mathrm{m}^2$$ separated by $$1.0\ \mathrm{mm} of $$air ($$K=1). $$What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\ \mathrm{F/m})$$

$$1.77 \times 10$$^{-10}$$\ \mathrm{F}$$

Question 1

Which of the following best describes the relationship between electric potential energy and electric potential for a point charge $$q at a $$position with potential $$V$$?

Accepted Answer

$$U = qV$$

Question 2

A parallel-plate capacitor is connected to a 12 V battery and has a capacitance of $$4\ \mu\mathrm{F}. $$How much energy is stored in the capacitor?

Accepted Answer

$$2.88 	imes 10$$^{-4}$$\ \mathrm{J}$$

Question 3

Which of the following statements about equipotential lines is correct?

Accepted Answer

Equipotential lines never cross each other.

Question 4

A $$2.0\ \mu\mathrm{F}$$ and a $$6.0\ \mu\mathrm{F}$$ capacitor are connected in series across a $$12\ \mathrm{V}$$ battery. What is the equivalent capacitance?

Accepted Answer

$$1.5\ \mu\mathrm{F}$$

Question 5

Which of the following best explains why lightning arcs require very high energies?

Accepted Answer

They span large electric potentials, requiring billions of joules to move charge across the air gap.

Question 6

A $$5.0\ \mu\mathrm{F}$$ capacitor is charged to $$10\ \mathrm{V}$$ and then disconnected from the battery. If a dielectric with $$K=2 is $$inserted, what is the new capacitance?

Accepted Answer

$$10.0\ \mu\mathrm{F}$$

Question 7

Which of the following is the correct formula for the capacitance of a parallel-plate capacitor with area $$A$$, plate separation $$d$$, and dielectric constant $$K$$?

Accepted Answer

$$C = K\$$varepsilon_0$$ \dfrac{A}{d}$$

Question 8

If the electric field between two parallel plates is $$E$$ and the distance between the plates is $$d$$, what is the potential difference $$V$$ between the plates?

Accepted Answer

$$V = Ed$$

Question 9

A $$3.0\ \mu\mathrm{F}$$ and a $$6.0\ \mu\mathrm{F}$$ capacitor are connected in parallel. What is their equivalent capacitance?

Accepted Answer

$$9.0\ \mu\mathrm{F}$$

Question 10

Which of the following is true about the work done by the electric field on a charge moving between two points with a potential difference $$\Delta V$$?

Accepted Answer

$$W = q\Delta V$$

Question 11

A $$10\ \mu\mathrm{F}$$ capacitor is charged to $$100\ \mathrm{V}. $$How much charge is stored on the capacitor?

Accepted Answer

$$1.0 	imes 10$$^{-3}$$\ \mathrm{C}$$

Question 12

Which of the following best describes the effect of inserting a dielectric material between the plates of a capacitor while it is connected to a battery?

Accepted Answer

The capacitance increases and the charge stored increases.

Question 13

Which of the following is the correct unit for capacitance?

Accepted Answer

Farad ($$\mathrm{F})$$

Question 14

A $$1.0\ \mu\mathrm{F}$$ capacitor and a $$2.0\ \mu\mathrm{F}$$ capacitor are connected in series across a $$12\ \mathrm{V}$$ battery. What is the voltage across the $$2.0\ \mu\mathrm{F}$$ capacitor?

Accepted Answer

$$8.0\ \mathrm{V}$$

Question 15

Which of the following is a correct statement about the energy stored in a capacitor?

Accepted Answer

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

Question 16

A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$50\ \mathrm{V}$$ and then disconnected from the battery. If the plate separation is doubled, what happens to the voltage across the capacitor?

Accepted Answer

It doubles to $$100\ \mathrm{V}.$$

Question 17

Which of the following is true about the electric field and equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces.

Question 18

A capacitor is constructed with plates of area $$0.02\ \mathrm{m}^2$$ separated by $$1.0\ \mathrm{mm} of $$air ($$K=1). $$What is its capacitance? ($$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{F/m})$$

Accepted Answer

$$1.77 	imes 10$$^{-10}$$\ \mathrm{F}$$

Question 19

Which of the following best describes the effect of connecting capacitors in parallel?

Accepted Answer

The equivalent capacitance increases and is the sum of the individual capacitances.

Question 20

A $$4.0\ \mu\mathrm{F}$$ capacitor is charged to $$20\ \mathrm{V}$$ and then connected in parallel with an uncharged $$2.0\ \mu\mathrm{F}$$ capacitor. What is the final voltage across both capacitors?

Accepted Answer

$$13.3\ \mathrm{V}$$

Electric Potential and Capacitance: Study Notes

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