Q: If a capacitor is discharged in $$10\ \mu\text{s}$$ and releases $$25\ \text{J} of $$energy, what is the average power dissipated?

$$P = 2.5 \times 10^6$\ \text{W}$$

Question 1

A parallel-plate capacitor is connected to a 1.5 V battery. The plates have an area $$A$$ and are separated by a distance $$d. $$Which equation correctly expresses the capacitance $$C of $$this capacitor?

Accepted Answer

$$C = \frac{\$$epsilon_0$$ A}{d}$$

Question 2

Which statement best describes Kirchhoff’s Loop Law in the context of electric circuits?

Accepted Answer

The sum of the potential differences around any closed loop is zero.

Question 3

A capacitor is charged to a voltage $$V$$ and then disconnected from the battery. If a dielectric with constant $$\kappa is $$inserted between the plates, what happens to the stored energy?

Accepted Answer

The stored energy remains unchanged.

Question 4

Which formula gives the energy $$U$$ stored in a capacitor with capacitance $$C$$ and voltage $$V$$?

Accepted Answer

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

Question 5

A spherical capacitor consists of two concentric spheres of radii $$R_1$$ and $$R_2$$ ($$R_2$$ \u003e $$R_1). $$What is the capacitance $$C$$?

Accepted Answer

$$C = 4\pi\$$epsilon_0$$ \frac{R_1$ R_2$}{R_2$ - R_1$}$$

Question 6

Three capacitors $$C_1$$, $$C_2$$, and $$C_3$$ are connected in parallel. What is the equivalent capacitance $$C_{eq}$$?

Accepted Answer

$$C_{eq} = C_1$ + C_2$ + C_3$

Question 7

In a series combination of capacitors, which quantity is the same for all capacitors?

Accepted Answer

Charge $$Q$$

Question 8

A defibrillator uses a capacitor to deliver a quick electric shock. If a $$2.0\ \mu	ext{F}$$ capacitor is charged to $$5000\ 	ext{V}$$, how much energy is stored?

Accepted Answer

$$U = 25\ 	ext{J}$$

Question 9

Which property of a dielectric material determines the maximum electric field it can sustain without breakdown?

Accepted Answer

Dielectric strength

Question 10

A parallel-plate capacitor is filled with a dielectric of constant $$\kappa. $$How does the capacitance change?

Accepted Answer

It increases by a factor of $$\kappa$$

Question 11

Which equation describes the electric field $$E$$ between the plates of a parallel-plate capacitor with surface charge density $$\sigma$$?

Accepted Answer

$$E = \frac{\sigma}{\$$epsilon_0$$}$$

Question 12

If a capacitor is discharged in $$10\ \mu	ext{s}$$ and releases $$25\ 	ext{J} of $$energy, what is the average power dissipated?

Accepted Answer

$$P = 2.5 	imes 10^6$\ 	ext{W}$$

Question 13

Which material would be best for a capacitor requiring a high dielectric constant and moderate dielectric strength?

Accepted Answer

Titanium dioxide

Question 14

What happens to the electric field inside a capacitor when a polarizable dielectric is inserted?

Accepted Answer

The electric field decreases

Question 15

A capacitor is made of two plates with area $$A$$ separated by distance $$d. If $$the plates are rolled up with a dielectric, what is the main advantage?

Accepted Answer

It allows for a compact, high-capacitance device

Question 16

Which equation gives the energy density $$u in $$the electric field between capacitor plates?

Accepted Answer

$$u = \frac{1}{2}\$$epsilon_0$$ E^2$

Question 17

In a circuit with capacitors $$C_1$$ and $$C_2 in $$series, and $$C_3 in $$parallel, which condition must be true after the switch is thrown to position B?

Accepted Answer

$$Q_1$$ + $$Q_2$$ = $$Q_3$$

Question 18

Which of the following is NOT a standard circuit element?

Accepted Answer

Dielectric

Potential, Electric Field, and Capacitors: Study Notes for College Physics

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