Q: A battery with emf $\varepsilon = 1.5\ \text{V}$ and internal resistance $r = 0.5\ \Omega$ supplies a current $I = 2.0\ \text{A}$ to a circuit. What is the terminal voltage across the battery?

$V = \varepsilon - Ir = 0.5\ \text{V}$

Q: If the resistance of a copper wire at $20^\circ\text{C}$ is $1.02\ \Omega$ and the temperature coefficient $\alpha = 0.0039\ \text{(C}^\circ\text{)}^{-1}$, what is the resistance at $100^\circ\text{C}$?

$R_{100} = R_0[1 + \alpha(T - T_0)] = 1.02[1 + 0.0039 \times 80] \approx 1.34\ \Omega$

Q: A patient undergoing heart surgery has a heart resistance of $250\ \Omega$. What is the minimum voltage that poses a danger if a current of $25\ \mu\text{A}$ passes through the heart?

$V = IR = 25 \times 10^{-6} \times 250 = 0.00625\ \text{V}$

Q: A battery with emf $\varepsilon = 12\ \text{V}$ and internal resistance $r = 2\ \Omega$ is connected to a $4\ \Omega$ resistor. What is the current in the circuit?

$I = \frac{\varepsilon}{R + r} = \frac{12}{6} = 2\ \text{A}$

Q: A nonideal battery of $10.0\ \text{V}$ with internal resistance $2.0\ \Omega$ is connected to a resistor $R = 10.0\ \Omega$. What is the current through the battery?

$I = \frac{10.0}{12.0} \approx 0.83\ \text{A}$

Question 1

Which of the following best describes the direction of conventional current in a metallic conductor?

Accepted Answer

It flows in the direction of positive charge movement.

Question 2

A copper wire of length $L = 20\ 	ext{m}$ and diameter $d = 1.3\ 	ext{mm}$ is used as a speaker wire. Given the resistivity of copper $ho = 1.72 	imes 10^{-8}\ \Omega \cdot 	ext{m}$, what is the resistance of the wire?

Accepted Answer

$R = \frac{\rho L}{A}$, where $A = \pi \left(\frac{d}{2}\right)^2$; $R \approx 0.26\ \Omega$

Question 3

Which material listed below would be most suitable for making electrical wires due to its low resistivity?

Accepted Answer

Silver

Question 4

A battery with emf $\varepsilon = 1.5\ 	ext{V}$ and internal resistance $r = 0.5\ \Omega$ supplies a current $I = 2.0\ 	ext{A}$ to a circuit. What is the terminal voltage across the battery?

Accepted Answer

$V = \varepsilon - Ir = 0.5\ 	ext{V}$

Question 5

If the resistance of a copper wire at $20^\circ	ext{C}$ is $1.02\ \Omega$ and the temperature coefficient $\alpha = 0.0039\ 	ext{(C}^\circ	ext{)}^{-1}$, what is the resistance at $100^\circ	ext{C}$?

Accepted Answer

$R_{100} = R_0[1 + \alpha(T - T_0)] = 1.02[1 + 0.0039 	imes 80] \approx 1.34\ \Omega$

Question 6

Which of the following statements about superconductors is correct?

Accepted Answer

Their resistivity drops to zero below a critical temperature $T_c$.

Question 7

A patient undergoing heart surgery has a heart resistance of $250\ \Omega$. What is the minimum voltage that poses a danger if a current of $25\ \mu	ext{A}$ passes through the heart?

Accepted Answer

$V = IR = 25 	imes 10^{-6} 	imes 250 = 0.00625\ 	ext{V}$

Question 8

Which of the following best describes the behavior of a semiconductor diode as shown in the $I$-$V$ graph?

Accepted Answer

It is a non-ohmic resistor, with $I$ increasing nonlinearly with $V$ in one direction.

Question 9

Three resistors $R_1 = 6\ \Omega$, $R_2 = 6\ \Omega$, and $R_3 = 6\ \Omega$ are connected as shown in a network with a battery of $18\ 	ext{V}$. What is the equivalent resistance of the network?

Accepted Answer

$R_{eq} = 9\ \Omega$

Question 10

In a parallel circuit, which of the following statements is true?

Accepted Answer

The potential difference across each resistor is the same.

Question 11

A battery with emf $\varepsilon = 12\ 	ext{V}$ and internal resistance $r = 2\ \Omega$ is connected to a $4\ \Omega$ resistor. What is the current in the circuit?

Accepted Answer

$I = \frac{\varepsilon}{R + r} = \frac{12}{6} = 2\ 	ext{A}$

Question 12

Which of the following is Kirchhoff’s junction rule?

Accepted Answer

$\sum I = 0$

Question 13

A nonideal battery of $10.0\ 	ext{V}$ with internal resistance $2.0\ \Omega$ is connected to a resistor $R = 10.0\ \Omega$. What is the current through the battery?

Accepted Answer

$I = \frac{10.0}{12.0} \approx 0.83\ 	ext{A}$

Question 14

Which of the following is true for resistors in series?

Accepted Answer

The current through each resistor is the same.

Question 15

A lightly coiled spring has 75 coils, each $3.50\ 	ext{cm}$ in diameter, made of wire $2.25\ 	ext{mm}$ in diameter. If the resistance measured is $1.74\ \Omega$, what is the resistivity of the metal?

Accepted Answer

$ho = \frac{RA}{L}$, where $L = 75 	imes \pi 	imes 3.50\ 	ext{cm}$ and $A = \pi \left(\frac{2.25\ 	ext{mm}}{2}ight)^2$; $ho \approx 1.7 	imes 10^{-7}\ \Omega \cdot 	ext{m}$

Question 16

Which of the following is the correct loop rule for a circuit containing a battery and resistors?

Accepted Answer

The sum of the potential differences in any loop is zero.

Question 17

A circuit contains a battery with emf $\varepsilon = 18\ 	ext{V}$ and three $6\ \Omega$ resistors arranged as shown in Example 19.9. What is the current through each resistor?

Accepted Answer

$I = 1\ 	ext{A}$

Question 18

In a real-world scenario, why does a flashlight become dim as its battery ages, even if the emf remains constant?

Accepted Answer

The internal resistance of the battery increases, reducing the terminal voltage.

Current, Resistance, and Direct-Current Circuits: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards