Q: A copper wire has a diameter of $1.02\ \mathrm{mm}$ and a free electron density of $8.5 \times 10^{28}\ \mathrm{m}^{-3}$. If the current through the wire is $0.801\ \mathrm{A}$, what is the drift velocity $v_d$ of the electrons? (Charge of electron $q = 1.6 \times 10^{-19}\ \mathrm{C}$)

$v_d = \dfrac{I}{nqA} = \dfrac{0.801}{8.5 \times 10^{28} \times 1.6 \times 10^{-19} \times \pi (0.00051)^2} \approx 1.15 \times 10^{-4}\ \mathrm{m/s}$

Q: A real battery has an emf $\mathcal{E}$ and internal resistance $r$. If the current in the circuit is $I$, what is the terminal voltage $V_{\text{terminal}}$ across the battery?

$V_{\text{terminal}} = \mathcal{E} - Ir$

Question 1

Which of the following best describes the direction of conventional current in a metal wire?

Accepted Answer

It is the direction that positive charge carriers would move.

Question 2

A copper wire has a diameter of $1.02\ \mathrm{mm}$ and a free electron density of $8.5 	imes 10^{28}\ \mathrm{m}^{-3}$. If the current through the wire is $0.801\ \mathrm{A}$, what is the drift velocity $v_d$ of the electrons? (Charge of electron $q = 1.6 	imes 10^{-19}\ \mathrm{C}$)

Accepted Answer

$v_d = \dfrac{I}{nqA} = \dfrac{0.801}{8.5 	imes 10^{28} 	imes 1.6 	imes 10^{-19} 	imes \pi (0.00051)^2} \approx 1.15 	imes 10^{-4}\ \mathrm{m/s}$

Question 3

Which equation correctly relates current $I$ to drift velocity $v_d$ in a conductor?

Accepted Answer

$I = n|q|v_dA$

Question 4

If a metal wire of resistance $R$ and resistivity $\rho$ has both its length and cross-sectional area cut in half, what will be its new resistance?

Accepted Answer

$R_{	ext{new}} = R$

Question 5

Which of the following statements about resistivity $\rho$ is correct?

Accepted Answer

Resistivity is an intrinsic property of a material and does not depend on the object's shape or size.

Question 6

A battery with emf $\mathcal{E}$ and internal resistance $r$ is connected to a resistor $R$. What is the current $I$ in the circuit?

Accepted Answer

$I = \dfrac{\mathcal{E}}{R + r}$

Question 7

Which device is used to measure the voltage difference across a circuit element, and what is its ideal resistance?

Accepted Answer

Voltmeter; infinite resistance

Question 8

The power delivered to a resistor in a circuit is given by which of the following equations?

Accepted Answer

$P = VI$

Question 9

A real battery has an emf $\mathcal{E}$ and internal resistance $r$. If the current in the circuit is $I$, what is the terminal voltage $V_{	ext{terminal}}$ across the battery?

Accepted Answer

$V_{	ext{terminal}} = \mathcal{E} - Ir$

Question 10

Which of the following best explains why the drift velocity of electrons in a conductor is much smaller than their average thermal velocity?

Accepted Answer

Electrons move randomly due to thermal energy, but the electric field only causes a small net bias in their motion.

Question 11

If the resistivity of a material increases with temperature, which type of material is it most likely to be?

Accepted Answer

A metal

Question 12

Which formula gives the temperature dependence of resistivity for a metal?

Accepted Answer

$\rho(T) = \rho_0 [1 + \alpha (T - T_0)]$

Question 13

A wire has resistance $R$ and resistivity $\rho$. If its length is doubled and its cross-sectional area is halved, what is its new resistance?

Accepted Answer

$R_{	ext{new}} = 4R$

Question 14

Which of the following is NOT a correct statement about Ohm's Law?

Accepted Answer

Ohm's Law applies to all materials, including diodes and semiconductors.

Question 15

In a circuit, if the current flows from point $a$ to point $b$ through a resistor, how does the electric potential change?

Accepted Answer

The electric potential decreases from $a$ to $b$.

Question 16

Which of the following best describes the role of electromotive force (emf) in a circuit?

Accepted Answer

It converts non-electrical energy (e.g., chemical) into electric potential energy.

Question 17

A voltmeter is connected across a resistor in a circuit. What property should the voltmeter have to minimize its effect on the circuit?

Accepted Answer

It should have a very high resistance.

Question 18

Which of the following is a correct expression for the rate of energy delivered to a circuit element?

Accepted Answer

$P = VI$

Question 19

If two copper wires of different diameters are joined end to end, what happens to the drift speed of electrons as they move from the larger-diameter wire into the smaller-diameter wire?

Accepted Answer

The drift speed increases.

Electric Current, Resistance, and Electromotive Force: Study Notes

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