Q: A parallel-plate capacitor is constructed with plates of area $$A = 2.00\ \mathrm{m}^2$$ separated by $$d = 5.00\ \mathrm{mm}$$ and connected to a $$10.0\ \mathrm{kV}$$ battery. What is the capacitance of this capacitor? (Assume air between the plates, $$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$\ \mathrm{C}^2/\mathrm{N}\cdot\mathrm{m}^2)$$

$$C = 3.54 \times 10$$^{-8}$$\ \mathrm{F}$$

Q: An electron is released from rest in a uniform electric field between two parallel plates separated by $$d = 6.36\ \mathrm{mm}$$ with $$E = 2.80 \times 10^3$\ \mathrm{N/C}. $$What is the work done by the electric force on the electron as it moves from the negative to the positive plate?

$$W = eEd = (1.6 \times 10$$^{-19}$$\ \mathrm{C})(2.80 \times 10^3$\ \mathrm{N/C})(6.36 \times 10$$^{-3}$$\ \mathrm{m}) = 2.85 \times 10$$^{-18}$$\ \mathrm{J}$$

Q: What is the electric potential energy of a system consisting of a $$+2e$$ charge and a $$-3e$$ charge separated by $$3\ \mathrm{nm}$$? ($$e = 1.6 \times 10$$^{-19}$$\ \mathrm{C}$$, $$k = 8.99 \times 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$)

$$U = -2.88 \times 10$$^{-18}$$\ \mathrm{J}$$

Question 1

A parallel-plate capacitor is constructed with plates of area $$A = 2.00\ \mathrm{m}^2$$ separated by $$d = 5.00\ \mathrm{mm}$$ and connected to a $$10.0\ \mathrm{kV}$$ battery. What is the capacitance of this capacitor? (Assume air between the plates, $$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$\ \mathrm{C}^2/\mathrm{N}\cdot\mathrm{m}^2)$$

Accepted Answer

$$C = 3.54 	imes 10$$^{-8}$$\ \mathrm{F}$$

Question 2

Which of the following statements about electric potential $$V$$ and electric potential energy $$U is $$correct?

Accepted Answer

$$U = q'V$$, where $$U is $$the potential energy of a charge $$q' at a $$point with potential $$V.$$

Question 3

A $$2\ \mu\mathrm{F}$$ and a $$6\ \mu\mathrm{F}$$ capacitor are connected in parallel across a $$12\ \mathrm{V}$$ battery. What is the ratio of the charges stored on the $$6\ \mu\mathrm{F}$$ and $$2\ \mu\mathrm{F}$$ capacitors ($$Q_6$$ : $$Q_2$$)?

Accepted Answer

$$3:1$$

Question 4

An electron is released from rest in a uniform electric field between two parallel plates separated by $$d = 6.36\ \mathrm{mm}$$ with $$E = 2.80 	imes 10^3$\ \mathrm{N/C}. $$What is the work done by the electric force on the electron as it moves from the negative to the positive plate?

Accepted Answer

$$W = eEd = (1.6 	imes 10$$^{-19}$$\ \mathrm{C})(2.80 	imes 10^3$\ \mathrm{N/C})(6.36 	imes 10$$^{-3}$$\ \mathrm{m}) = 2.85 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 5

A $$9\ \mathrm{V}$$ battery and a $$1.5\ \mathrm{V} AA $$cell are sitting on a table. Which one stores more energy?

Accepted Answer

Cannot be determined from voltage alone

Question 6

What is the electric potential energy of a system consisting of a $$+2e$$ charge and a $$-3e$$ charge separated by $$3\ \mathrm{nm}$$? ($$e = 1.6 	imes 10$$^{-19}$$\ \mathrm{C}$$, $$k = 8.99 	imes 10^9$\ \mathrm{N\cdot m^2$/C^2$$}$)

Accepted Answer

$$U = -2.88 	imes 10$$^{-18}$$\ \mathrm{J}$$

Question 7

A parallel-plate capacitor is connected to a battery and then the plate separation is doubled while the battery remains connected. What happens to the stored energy?

Accepted Answer

It drops to one quarter

Question 8

Which of the following best describes the effect of inserting a dielectric slab with dielectric constant $$\kappa \u003e 1$$ between the plates of a capacitor while the battery remains connected?

Accepted Answer

Capacitance increases, charge increases, voltage stays the same

Question 9

Which combination of capacitors will always result in an equivalent capacitance less than the smallest individual capacitance?

Accepted Answer

Capacitors in series

Question 10

A defibrillator contains a $$100\ \mu\mathrm{F}$$ capacitor charged to $$2.0\ \mathrm{kV}. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = 200\ \mathrm{J}$$

Question 11

Which of the following is true about equipotential surfaces?

Accepted Answer

Moving a charge along an equipotential surface requires no work.

Question 12

A $$4\ \mu\mathrm{F}$$ and a $$12\ \mu\mathrm{F}$$ capacitor are connected in series. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = 3\ \mu\mathrm{F}$$

Question 13

The energy per unit volume stored in an electric field $$E in $$vacuum is given by:

Accepted Answer

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

Question 14

A $$2.0\ \mu\mathrm{F}$$ capacitor is charged to $$12\ \mathrm{V}$$, then disconnected from the battery. A dielectric slab with $$\kappa = 3 is $$inserted. What is the new voltage across the capacitor?

Accepted Answer

$$4.0\ \mathrm{V}$$

Question 15

Which of the following best describes the direction of the electric field in a region where the electric potential increases in the $$+x$$ direction?

Accepted Answer

The electric field points in the $$-x$$ direction.

Question 16

A parallel-plate capacitor has a plate area $$A$$ and separation $$d. If $$both $$A$$ and $$d$$ are doubled, what happens to the capacitance?

Accepted Answer

It stays the same

Question 17

A test charge $$q' is $$placed at a point where the electric potential due to several point charges is $$V = 100\ \mathrm{V}. $$What is the potential energy of the test charge?

Accepted Answer

$$U = 100q'$$

Question 18

Which material would provide the largest increase in capacitance if used as a dielectric in a parallel-plate capacitor?

Accepted Answer

Strontium titanate ($$\kappa = 300)$$

Question 19

A $$6.0\ \mu\mathrm{F}$$ and a $$3.0\ \mu\mathrm{F}$$ capacitor are connected in parallel across an $$18\ \mathrm{V}$$ battery. What is the total charge stored in the system?

Accepted Answer

$$Q = 162\ \mu\mathrm{C}$$

Electric Potential and Capacitance: Study Notes for Physics with Calculus

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