Q: A $$2.0\,\mu F$$ and a $$3.0\,\mu F$$ capacitor are connected in parallel across a $$12\,V$$ battery. What is the total charge stored in the system?

$$Q = (C_1$ + C_2$)V = (2.0 + 3.0)\times 10$$^{-6}$$ \times 12 = 60\,\mu C$$

Q: A $$1.0\,\mu F$$ capacitor is charged to $$10\,V. $$How much energy is stored in the capacitor?

$$U = \frac{1}{2}CV^2$ = \frac{1}{2} \times 1.0 \times 10$$^{-6}$$ \times 10^2$ = 5.0 \times 10$$^{-5}$$ J$$

Question 1

A 9 V battery is used to power a small electronic device. What is the meaning of the 9 V rating in terms of electric potential?

Accepted Answer

It means the battery can supply 9 joules of energy to every coulomb of charge that passes through it. $$V = \frac{U}{q}$$

Question 2

Which of the following correctly expresses the electric potential energy $$U of a $$charge $$q' at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$U = k \frac{q q'}{r}$$

Question 3

A positive charge moves in the direction of a uniform electric field $$\vec{E}. $$What happens to its electric potential energy and why?

Accepted Answer

Its electric potential energy decreases because the field does positive work on the charge.

Question 4

What is the capacitance $$C of a $$parallel-plate capacitor with plate area $$A$$ and separation $$d in $$vacuum?

Accepted Answer

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

Question 5

Two capacitors, $$C_1 = 4$$\,\mu F$$ and C_2$ = 6\,\mu F$$, are connected in series. What is their equivalent capacitance?

Accepted Answer

$$C_{eq} = \frac{1}{\frac{1}{C_1$} + \frac{1}{C_2$}} = 2.4\,\mu F$$

Question 6

A parallel-plate capacitor is charged to a potential difference $$V$$ and then disconnected from the battery. If a dielectric with dielectric constant $$K is $$inserted between the plates, what happens to the capacitance and the potential difference?

Accepted Answer

Capacitance increases by a factor of $$K$$, and the potential difference decreases by a factor of $$K if $$the charge remains constant.

Question 7

Which of the following best describes an equipotential surface?

Accepted Answer

A surface on which the electric potential is the same at every point.

Question 8

A $$2.0\,\mu F$$ and a $$3.0\,\mu F$$ capacitor are connected in parallel across a $$12\,V$$ battery. What is the total charge stored in the system?

Accepted Answer

$$Q = (C_1$ + C_2$)V = (2.0 + 3.0)	imes 10$$^{-6}$$ 	imes 12 = 60\,\mu C$$

Question 9

A point charge $$q$$ creates an electric potential $$V at a $$distance $$r. If $$the distance is doubled, what happens to the potential?

Accepted Answer

It is reduced to half: $$V' = \frac{kq}{2r}$$

Question 10

A $$1.0\,\mu F$$ capacitor is charged to $$10\,V. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = \frac{1}{2} 	imes 1.0 	imes 10$$^{-6}$$ 	imes 10^2$ = 5.0 	imes 10$$^{-5}$$ J$$

Question 11

A $$2.0\,\mu F$$ and a $$4.0\,\mu F$$ capacitor are connected in series across a $$24\,V$$ battery. What is the voltage across the $$4.0\,\mu F$$ capacitor?

Accepted Answer

$$V_2$$ = $$Q/C_2 = 16$$\,V$$

Question 12

Which of the following is true about the energy density $$u in $$the electric field between the plates of a parallel-plate capacitor?

Accepted Answer

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

Question 13

A $$5.0\,\mu F$$ capacitor is charged to $$20\,V$$ and then disconnected from the battery. If the plate separation is doubled, what happens to the energy stored in the capacitor?

Accepted Answer

It increases by a factor of 2.

Question 14

Which of the following statements about capacitors in parallel is correct?

Accepted Answer

The equivalent capacitance is the sum of the individual capacitances: $$C_{eq} = C_1$ + C_2$ + ...$$

Question 15

A $$3.0\,\mu F$$ and a $$6.0\,\mu F$$ capacitor are connected in series across a $$12\,V$$ battery. What is the charge on each capacitor?

Accepted Answer

$$Q = C_{eq} V = 4.0\,\mu C$$

Question 16

A $$1.0\,\mu F$$ capacitor and a $$2.0\,\mu F$$ capacitor are connected in parallel to a $$10\,V$$ battery. What is the total energy stored in the system?

Accepted Answer

$$U = \frac{1}{2} C_{eq} V^2$ = 1.5 	imes 10$$^{-5}$$ J$$

Question 17

A $$2.0\,\mu F$$ capacitor is charged to $$100\,V$$ and then connected in parallel with an uncharged $$2.0\,\mu F$$ capacitor. What is the final voltage across both capacitors?

Accepted Answer

$$V = 50\,V$$

Question 18

Which of the following is a correct expression for the work done by an electric field on a charge $$q$$ moving a distance $$s in $$the direction of the field?

Accepted Answer

$$W = qEs$$

Chapter 18: Electric Potential and Capacitance – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard