Q: A copper wire has a length of 65 m and a diameter of 2 mm. If the resistivity of copper is $$1.69 \times 10$$^{-8}$$ \ \Omega \mathrm{m}$$, what is the resistance of the wire?

$$R = \frac{\rho L}{A} = \frac{1.69 \times 10$$^{-8}$$ \times 65}{\pi (0.001)^2$} = 0.35 \ \Omega$$

Q: A 60 W incandescent light bulb is on for 5 hours a day for 30 days. How much energy is used by the light bulb in kilowatt-hours (kWh)?

$$E = P \times t = 60 \ \mathrm{W} \times 150 \ \mathrm{h} = 9000 \ \mathrm{Wh} = 9 \ \mathrm{kWh}$$

Q: If the power company charges $$0.10$$ per kWh, how much will the energy used in the previous question cost?

$$\text{Cost} = 9 \ \mathrm{kWh} \times 0.10 = \0.90$

Question 1

A copper wire has a length of 65 m and a diameter of 2 mm. If the resistivity of copper is $$1.69 	imes 10$$^{-8}$$ \ \Omega \mathrm{m}$$, what is the resistance of the wire?

Accepted Answer

$$R = \frac{ho L}{A} = \frac{1.69 	imes 10$$^{-8}$$ 	imes 65}{\pi (0.001)^2$} = 0.35 \ \Omega$$

Question 2

A 120 V power supply is connected to the copper wire in the previous question. What is the magnitude of the current in the wire?

Accepted Answer

$$I = \frac{V}{R} = \frac{120}{0.35} = 343 \ \mathrm{A}$$

Question 3

Which of the following best describes the effect of increasing the cross-sectional area of a wire on its resistance?

Accepted Answer

The resistance decreases because $$R = \frac{\rho L}{A}.$$

Question 4

A battery with an emf of 12 V and internal resistance of $$0.5 \ \Omega is $$connected in series to a $$15 \ \Omega$$ resistor. What is the current in the circuit?

Accepted Answer

$$I = \frac{\varepsilon}{R + r} = \frac{12}{15 + 0.5} = 0.77 \ \mathrm{A}$$

Question 5

A 60 W incandescent light bulb is on for 5 hours a day for 30 days. How much energy is used by the light bulb in kilowatt-hours (kWh)?

Accepted Answer

$$E = P 	imes t = 60 \ \mathrm{W} 	imes 150 \ \mathrm{h} = 9000 \ \mathrm{Wh} = 9 \ \mathrm{kWh}$$

Question 6

If the power company charges $$0.10$$ per kWh, how much will the energy used in the previous question cost?

Accepted Answer

$$	ext{Cost} = 9 \ \mathrm{kWh} 	imes 0.10 = \0.90$

Question 7

Which of the following statements about conventional current and electron flow is correct?

Accepted Answer

Conventional current is defined as the flow of positive charge, which is opposite to the direction of electron flow in a wire.

Question 8

A series circuit contains two resistors, $$R_1 = 5$$ \ \Omega$$ and R_2$ = 3 \ \Omega$$, connected to a $$9 \ \mathrm{V}$$ battery. What is the total current in the circuit?

Accepted Answer

$$I = \frac{V}{R_1$ + R_2$} = \frac{9}{8} = 1.1 \ \mathrm{A}$$

Question 9

In a parallel circuit, $$R_1 = 3$$ \ \Omega$$ and R_2$ = 6 \ \Omega$$ are connected to an $$18 \ \mathrm{V}$$ battery. What is the equivalent resistance of the circuit?

Accepted Answer

$$\frac{1}{R_{eq}} = \frac{1}{3} + \frac{1}{6} \Rightarrow R_{eq} = 2 \ \Omega$$

Question 10

A voltmeter is used to measure the voltage across a battery in a circuit. How should it be connected?

Accepted Answer

In parallel with the battery terminals.

Question 11

A 25 $$\Omega$$ resistor is connected across a battery with internal resistance $$0.6 \Omega. If $$the current in the circuit is $$0.75 A$$, what is the EMF of the battery?

Accepted Answer

$$\varepsilon = I(R + r) = 0.75 	imes (25 + 0.6) = 19.2 \ \mathrm{V}$$

Question 12

Which material below has the lowest resistivity and is therefore the best conductor?

Accepted Answer

Silver

Question 13

A circuit contains three resistors: $$R_1 = 10$$ \Omega$$, R_2$ = 8 \Omega in $$series, and $$R_3 = 6$$ \Omega$$ in parallel with the series combination. What is the equivalent resistance?

Accepted Answer

$$R_{eq} = \frac{R_{12} 	imes R_3$}{R_{12} + R_3$} = \frac{18 	imes 6}{18 + 6} = 4.5 \Omega$$

Question 14

A 6 V battery with internal resistance $$1.5 \Omega is $$connected in series to a light bulb with resistance $$6.8 \Omega. $$What is the terminal voltage of the battery when the circuit is operating?

Accepted Answer

$$V_T = \varepsilon - Ir = 6 - (0.72 	imes 1.5) = 4.9 \mathrm{V}$$

Question 15

Which of the following changes will NOT affect the resistivity ($$\rho) of a $$copper wire?

Accepted Answer

Doubling the radius of the wire.

Question 16

A student wants to maximize the power delivered to two heating coils (each $$17.3 \Omega) $$using a 12 V battery with $$0.5 \Omega$$ internal resistance. How should the coils be connected?

Accepted Answer

In parallel, to minimize the net resistance.

Question 17

A circuit contains a battery (emf $$\varepsilon$$ and internal resistance $$r) $$and an external resistor $$R. $$Which equation gives the terminal voltage $$V_T$$?

Accepted Answer

$$V_T = \varepsilon - Ir$$

Electric Current and DC Circuits: Comprehensive Study Notes

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