Q: A parallel plate capacitor is connected to a 15 V battery. If the surface area of each plate is $$0.02 \text{ m}^2$$ and the distance between the plates is $$0.001 \text{ m}$$, what is the capacitance of the capacitor? (Assume vacuum between plates, $$\$$varepsilon_0$$ = 8.85 \times 10$$^{-12}$$ \text{ F/m})$$

$$C = \dfrac{\$$varepsilon_0$$ A}{d} = \dfrac{8.85 \times 10$$^{-12}$$ \times 0.02}{0.001} = 1.77 \times 10$$^{-10}$$ \text{ F}$$

Q: A $$10 \text{ mF}$$ capacitor is connected to a $$20 \text{ V}$$ battery. How much charge accumulates on each plate?

$$Q = CV = 10 \times 10$$^{-3}$$ \times 20 = 0.2 \text{ C}$$

Q: A $$5 \text{ mF}$$ capacitor is charged to $$12 \text{ V}$$ and then disconnected from the battery. If a dielectric with $$k = 3 is $$inserted, what is the new voltage across the capacitor?

$$V_{new} = \dfrac{V_{old}}{k} = \dfrac{12}{3} = 4 \text{ V}$$

Q: A resistor has a resistance of $$10 \Omega$$ and is connected to a $$5 \text{ V}$$ battery. What is the current through the resistor?

$$I = \dfrac{V}{R} = \dfrac{5}{10} = 0.5 \text{ A}$$

Q: What is the equivalent resistance of two resistors, $$R_1 = 4$$ \Omega$$ and R_2$ = 6 \Omega$$, connected in parallel?

$$R_{eq} = \dfrac{R_1$ R_2$}{R_1$ + R_2$} = \dfrac{4 \times 6}{4 + 6} = 2.4 \Omega$$

Q: A $$12 \text{ V}$$ battery is connected to a circuit with a total resistance of $$3 \Omega. $$What is the power delivered to the circuit?

$$P = \dfrac{V^2$}{R} = \dfrac{12^2$}{3} = 48 \text{ W}$$

Question 1

A parallel plate capacitor is connected to a 15 V battery. If the surface area of each plate is $$0.02 	ext{ m}^2$$ and the distance between the plates is $$0.001 	ext{ m}$$, what is the capacitance of the capacitor? (Assume vacuum between plates, $$\$$varepsilon_0$$ = 8.85 	imes 10$$^{-12}$$ 	ext{ F/m})$$

Accepted Answer

$$C = \dfrac{\$$varepsilon_0$$ A}{d} = \dfrac{8.85 	imes 10$$^{-12}$$ 	imes 0.02}{0.001} = 1.77 	imes 10$$^{-10}$$ 	ext{ F}$$

Question 2

If a capacitor with capacitance $$C is $$charged to a voltage $$V$$, what is the energy stored in the capacitor?

Accepted Answer

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

Question 3

A $$10 	ext{ mF}$$ capacitor is connected to a $$20 	ext{ V}$$ battery. How much charge accumulates on each plate?

Accepted Answer

$$Q = CV = 10 	imes 10$$^{-3}$$ 	imes 20 = 0.2 	ext{ C}$$

Question 4

If the distance between the plates of a parallel plate capacitor is doubled, what happens to the capacitance?

Accepted Answer

It is halved.

Question 5

A dielectric with relative permittivity $$k = 2 is $$inserted between the plates of a capacitor. How does the capacitance change?

Accepted Answer

It doubles.

Question 6

Which equation correctly relates the charge $$Q$$, capacitance $$C$$, and voltage $$V$$ for a capacitor?

Accepted Answer

$$Q = CV$$

Question 7

A $$5 	ext{ mF}$$ capacitor is charged to $$12 	ext{ V}$$ and then disconnected from the battery. If a dielectric with $$k = 3 is $$inserted, what is the new voltage across the capacitor?

Accepted Answer

$$V_{new} = \dfrac{V_{old}}{k} = \dfrac{12}{3} = 4 	ext{ V}$$

Question 8

Which of the following best describes the function of a capacitor in a circuit?

Accepted Answer

It stores electrical energy and can release it when needed.

Question 9

A resistor has a resistance of $$10 \Omega$$ and is connected to a $$5 	ext{ V}$$ battery. What is the current through the resistor?

Accepted Answer

$$I = \dfrac{V}{R} = \dfrac{5}{10} = 0.5 	ext{ A}$$

Question 10

Which of the following materials would have the lowest resistivity?

Accepted Answer

Copper

Question 11

If a wire's length is doubled and its cross-sectional area is halved, how does its resistance change?

Accepted Answer

It increases by a factor of 4.

Question 12

A $$100 	ext{ W}$$ lightbulb and a $$60 	ext{ W}$$ lightbulb are connected in parallel to a $$120 	ext{ V}$$ source. Which bulb has the higher resistance?

Accepted Answer

The $$60 	ext{ W}$$ bulb

Question 13

What is the total resistance of three resistors, $$R_1 = 2$$ \Omega$$, R_2$ = 3 \Omega$$, and $$R_3 = 5$$ \Omega$$, connected in series?

Accepted Answer

$$R_{eq} = R_1$ + R_2$ + R_3$ = 2 + 3 + 5 = 10 \Omega$$

Question 14

What is the equivalent resistance of two resistors, $$R_1 = 4$$ \Omega$$ and R_2$ = 6 \Omega$$, connected in parallel?

Accepted Answer

$$R_{eq} = \dfrac{R_1$ R_2$}{R_1$ + R_2$} = \dfrac{4 	imes 6}{4 + 6} = 2.4 \Omega$$

Question 15

A $$12 	ext{ V}$$ battery is connected to a circuit with a total resistance of $$3 \Omega. $$What is the power delivered to the circuit?

Accepted Answer

$$P = \dfrac{V^2$}{R} = \dfrac{12^2$}{3} = 48 	ext{ W}$$

Question 16

Which statement about conventional current is correct?

Accepted Answer

It flows from the positive terminal to the negative terminal.

Question 17

If a capacitor is discharged through a resistor, what happens to the current over time?

Accepted Answer

It decreases exponentially.

Question 18

A wire has a resistance $$R$$ and is connected to a battery of emf $$\mathcal{E}. If $$the wire is replaced with another of the same material but twice the length and half the cross-sectional area, what is the new resistance?

Accepted Answer

$$R_{new} = 4R$$

Unit 11: Electric Circuits – Capacitors, Voltage, and Energy

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