Q: A metal sphere of radius $$0.1\ m is $$charged to the breakdown voltage of air ($$3 \times 10^6$\ V/m). $$What is the maximum charge it can hold?

$$Q = rE/k = 0.1 \times 3 \times 10^6$ / 9 \times 10^9$ = 3.3 \times 10$$^{-5}$$\ C$$

Q: Two capacitors, $$C_1 = 10$$\ nF$$ at 12$$\ V$$ and C_2$ = 20\ nF at$$ $$10\ V$$, are charged and then disconnected from their batteries and connected together (same polarity). What is the final voltage across both capacitors?

$$V_f = \frac{C_1V_1 + C_2V_2}{C_1$ + C_2$} = \frac{(10 \times 12) + (20 \times 10)}{10 + 20} = 10.67\ V$$

Q: A $$6.5\ nF$$ capacitor is connected to a $$12\ V$$ battery. What is the charge stored on the capacitor?

$$Q = CV = 6.5 \times 10$$^{-9}$$ \times 12 = 7.8 \times 10$$^{-8}$$\ C$$

Q: The electron volt (eV) is a unit of energy. How much energy in joules does $$1\ eV$$ correspond to?

$$1\ eV = 1.6 \times 10$$^{-19}$$\ J$$

Question 1

Which of the following best describes the relationship between electric potential energy and work done by the electric field when moving a charge from point A to point B?

Accepted Answer

$$PE_A - PE_B = -W_{ba}$$

Question 2

A proton is moved from point A to point B in a uniform electric field. If the displacement is $$d$$ and the field strength is $$E$$, what is the change in electric potential energy?

Accepted Answer

$$\Delta U_E = qEd$$

Question 3

Which of the following statements about equipotential lines is correct?

Accepted Answer

Equipotential lines are always perpendicular to electric field lines.

Question 4

The electric potential $$V at a $$distance $$r$$ from a point charge $$Q is $$given by which formula?

Accepted Answer

$$V = kQ/r$$

Question 5

A parallel plate capacitor is constructed with plate area $$A$$ and separation $$d. $$What is the capacitance if the space between the plates is filled with a dielectric of constant $$K$$?

Accepted Answer

$$C = K\$$varepsilon_0$$ A/d$$

Question 6

A camera flash uses a $$150\ \mu F$$ capacitor charged to $$200\ V. $$How much energy is stored in the capacitor?

Accepted Answer

$$U = \frac{1}{2}CV^2$ = 3.0\ J$$

Question 7

If the voltage across a capacitor is doubled, by what factor does the energy stored in the capacitor change?

Accepted Answer

It increases by a factor of 4.

Question 8

What is the unit of capacitance and how is it defined in terms of SI base units?

Accepted Answer

Farad ($$F$$), $$1\ F = 1\ C/V$$

Question 9

A metal sphere of radius $$0.1\ m is $$charged to the breakdown voltage of air ($$3 	imes 10^6$\ V/m). $$What is the maximum charge it can hold?

Accepted Answer

$$Q = rE/k = 0.1 	imes 3 	imes 10^6$ / 9 	imes 10^9$ = 3.3 	imes 10$$^{-5}$$\ C$$

Question 10

Which of the following best explains why inserting a dielectric between the plates of a charged, isolated capacitor increases its capacitance?

Accepted Answer

The dielectric reduces the effective electric field, allowing more charge to be stored for the same voltage.

Question 11

Two capacitors, $$C_1 = 10$$\ nF$$ at 12$$\ V$$ and C_2$ = 20\ nF at$$ $$10\ V$$, are charged and then disconnected from their batteries and connected together (same polarity). What is the final voltage across both capacitors?

Accepted Answer

$$V_f = \frac{C_1V_1 + C_2V_2}{C_1$ + C_2$} = \frac{(10 	imes 12) + (20 	imes 10)}{10 + 20} = 10.67\ V$$

Question 12

The energy density $$u$$ stored in the electric field between the plates of a parallel plate capacitor is given by:

Accepted Answer

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

Question 13

Which of the following is true about the electric potential due to a dipole at a point far from the dipole?

Accepted Answer

It falls off as $$1/r^2.$$

Question 14

A $$6.5\ nF$$ capacitor is connected to a $$12\ V$$ battery. What is the charge stored on the capacitor?

Accepted Answer

$$Q = CV = 6.5 	imes 10$$^{-9}$$ 	imes 12 = 7.8 	imes 10$$^{-8}$$\ C$$

Question 15

If a dielectric is inserted into a capacitor that remains connected to a battery, what happens to the charge on the plates?

Accepted Answer

The charge increases.

Question 16

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

Accepted Answer

Water ($$K \approx 80)$$

Question 17

The electron volt (eV) is a unit of energy. How much energy in joules does $$1\ eV$$ correspond to?

Accepted Answer

$$1\ eV = 1.6 	imes 10$$^{-19}$$\ J$$

Question 18

Which of the following is NOT a typical application of capacitors?

Accepted Answer

Generating continuous current in a circuit.

Electrical Potential, Electrical Energy, and Capacitance – Study Notes

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