Q: A $100\ \mathrm{pF}$ parallel-plate capacitor is to be constructed using plates separated by $0.2\ \mathrm{mm}$. What plate area $A$ is required? ($\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F/m}$)

$2.26\times 10^{-2}\ \mathrm{m}^2$

Q: A $10\ \mu\mathrm{F}$ capacitor and a $20\ \mu\mathrm{F}$ capacitor are connected in parallel across a $12\ \mathrm{V}$ battery. What is the total energy stored in the capacitors?

$2.16\times 10^{-3}\ \mathrm{J}$

Question 1

Which of the following correctly expresses the relationship between electric field $\vec{E}$ and electric potential $V$ along a path $ds$?

Accepted Answer

$dV = -\vec{E} \cdot d\vec{s}$

Question 2

A parallel-plate capacitor has plates of area $A$ separated by distance $d$ and is filled with a dielectric of constant $\kappa$. What is the correct formula for its capacitance $C$?

Accepted Answer

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

Question 3

A 9.0 V battery does 27 J of work moving charge from its negative to positive terminal. How much charge is transferred?

Accepted Answer

$3.0\ \mathrm{C}$

Question 4

If the electric field $E$ between two parallel plates is $2.0 	imes 10^4\ \mathrm{V/m}$ and the plates are $0.01\ \mathrm{m}$ apart, what is the potential difference $\Delta V$ between the plates?

Accepted Answer

$200\ \mathrm{V}$

Question 5

Which of the following statements about conductors in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside the conductor is zero.

Question 6

Two capacitors, $C_1 = 2\ \mu\mathrm{F}$ and $C_2 = 4\ \mu\mathrm{F}$, are connected in series. What is their equivalent capacitance?

Accepted Answer

$1.33\ \mu\mathrm{F}$

Question 7

A parallel-plate capacitor is charged to a potential $V$ and then disconnected from the battery. If a dielectric with $\kappa = 3$ is inserted between the plates, what happens to the stored energy?

Accepted Answer

It decreases by a factor of 3.

Question 8

Which of the following best describes the energy stored in a capacitor of capacitance $C$ charged to a voltage $V$?

Accepted Answer

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

Question 9

A capacitor is constructed using two square plates of side $L$ separated by a distance $d$. If the area of the plates is doubled and the separation is halved, how does the capacitance change?

Accepted Answer

It increases by a factor of 4.

Question 10

Which of the following is a reason for using a dielectric in a capacitor?

Accepted Answer

To increase the maximum operating voltage

Question 11

A $100\ \mathrm{pF}$ parallel-plate capacitor is to be constructed using plates separated by $0.2\ \mathrm{mm}$. What plate area $A$ is required? ($\varepsilon_0 = 8.85 	imes 10^{-12}\ \mathrm{F/m}$)

Accepted Answer

$2.26	imes 10^{-2}\ \mathrm{m}^2$

Question 12

If the potential difference across a $5\ \mu\mathrm{F}$ capacitor is $12\ \mathrm{V}$, what is the charge stored on the capacitor?

Accepted Answer

$60\ \mu\mathrm{C}$

Question 13

A parallel-plate capacitor with air between the plates is charged to $200\ \mathrm{V}$. The plate area is $0.01\ \mathrm{m}^2$ and the separation is $0.5\ \mathrm{mm}$. What is the energy density in the electric field between the plates?

Accepted Answer

$0.354\ \mathrm{J/m}^3$

Question 14

Which of the following is true for capacitors connected in parallel?

Accepted Answer

The total charge is the sum of the charges on each capacitor.

Question 15

A Van de Graaff generator is an example of which of the following?

Accepted Answer

A device that separates charge mechanically

Question 16

If the electric field in a region is given by $E = -\dfrac{dV}{dx}$, what does a negative slope of $V$ vs $x$ indicate about the direction of $E$?

Accepted Answer

The electric field points in the direction of increasing $x$.

Question 17

A capacitor is connected to a battery and fully charged. The battery is then removed, and a dielectric is inserted. Which of the following quantities remains unchanged?

Accepted Answer

The charge on the capacitor

Question 18

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

Accepted Answer

Polystyrene

Question 19

A $10\ \mu\mathrm{F}$ capacitor and a $20\ \mu\mathrm{F}$ capacitor are connected in parallel across a $12\ \mathrm{V}$ battery. What is the total energy stored in the capacitors?

Accepted Answer

$2.16	imes 10^{-3}\ \mathrm{J}$

Electric Potential, Electric Field, and Capacitors – Chapter 26 Study Notes

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