Question 1

A parallel-plate capacitor has plates separated by a distance $$d$$ and carries charge $$Q on $$each plate. What is the potential difference $$V$$ between the plates?

Accepted Answer

$$V = \dfrac{Qd}{\$$varepsilon_0$$ A}$$

Question 2

Which of the following statements about equipotential surfaces is correct?

Accepted Answer

Equipotential surfaces are surfaces that have the same value of potential at every point.

Question 3

The electric field at a point is related to the electric potential by which of the following expressions?

Accepted Answer

$$E_x = -\dfrac{dV}{dx}$$

Question 4

A solid sphere of radius $$R$$ carries a uniformly distributed charge $$Q. $$What is the electric potential at the center of the sphere, relative to infinity?

Accepted Answer

$$V(0) = \dfrac{3Q}{8\pi \$$varepsilon_0$$ R}$$

Question 5

If the electric potential is constant in a region of space, what can be said about the electric field in that region?

Accepted Answer

The electric field is zero.

Question 6

A capacitor is charged to $$V_0$$ and stores energy $$U_0. If $$the voltage is doubled to $$2V_0$$, what is the new stored energy?

Accepted Answer

$$U = 4U_0$$

Question 7

A point charge $$q is $$located at the origin. What is the electric potential at a distance $$r$$ from the charge, taking $$V=0 at $$infinity?

Accepted Answer

$$V(r) = \dfrac{q}{4\pi \$$varepsilon_0$$ r}$$

Question 8

Two conducting spheres are connected by a metal wire. Which quantity must be the same for both spheres?

Accepted Answer

Same potential

Question 9

A parallel-plate capacitor has area $$A$$ and plate separation $$d. If a $$dielectric with constant $$k is $$inserted between the plates, what is the new capacitance?

Accepted Answer

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

Question 10

Which of the following best describes the effect of inserting a dielectric between the plates of a capacitor?

Accepted Answer

It increases the capacitance by a factor equal to the dielectric constant.

Question 11

A battery maintains a potential difference between its terminals by converting which type of energy into electrical energy?

Accepted Answer

Chemical energy

Question 12

Three capacitors of $$2\,\mu\mathrm{F}$$, $$3\,\mu\mathrm{F}$$, and $$6\,\mu\mathrm{F}$$ are connected in parallel. What is the equivalent capacitance?

Accepted Answer

$$11\,\mu\mathrm{F}$$

Question 13

Two capacitors, $$C_1 = 2.0$$\,\mu\mathrm{F}$$ and C_2$ = 6.0\,\mu\mathrm{F}$$, are connected in series. What is the equivalent capacitance?

Accepted Answer

$$C_{eq} = 1.5\,\mu\mathrm{F}$$

Question 14

An electron is released from rest at $$x = 2\,\mathrm{m} in a $$region where the electric potential decreases with increasing $$x. $$What does the electron do immediately after being released?

Accepted Answer

It moves to the left with increasing speed.

Question 15

The energy stored in a parallel-plate capacitor is given by which of the following formulas?

Accepted Answer

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

Question 16

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

Accepted Answer

It decreases by a factor equal to the dielectric constant.

Question 17

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

Accepted Answer

The electric field is always perpendicular to an equipotential surface.

Question 18

A parallel-plate capacitor has plate area $$A$$ and separation $$d. $$What is the capacitance?

Accepted Answer

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

Question 19

A capacitor stores charge $$Q at $$potential difference $$V. $$Which equation correctly relates these quantities?

Accepted Answer

$$Q = C V$$

Electric Potential and Capacitance (Chapter 26) – Study Notes

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