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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