Q: A copper wire of cross-sectional area $$1.00 \times 10$$^{-6}$$\ \mathrm{m}^2$$ carries a current of $$2.0\ \mathrm{A}. If $$the number density of conduction electrons in copper is $$1.10 \times 10$$^{29}$$\ \mathrm{m}^{-3}$$, what is the drift speed of the electrons?

$$1.1 \times 10$$^{-4}$$\ \mathrm{m/s}$$

Q: A resistor has a resistance of $$19.8\ \Omega at$$ $$15.0^\circ\mathrm{C}$$ and $$25.0\ \Omega at$$ $$85.0^\circ\mathrm{C}. $$What is the temperature coefficient of resistivity $$\alpha$$?

$$3.75 \times 10$$^{-3}$$\ ^\circ\mathrm{C}^{-1}$$

Q: A current of $$80.0\ \mathrm{mA}$$ flows through a wire for $$10.0$$ minutes. How many electrons pass through a cross-section of the wire in this time?

$$3.00 \times 10$$^{20}$$ electrons

Question 1

A copper wire of cross-sectional area $$1.00 	imes 10$$^{-6}$$\ \mathrm{m}^2$$ carries a current of $$2.0\ \mathrm{A}. If $$the number density of conduction electrons in copper is $$1.10 	imes 10$$^{29}$$\ \mathrm{m}^{-3}$$, what is the drift speed of the electrons?

Accepted Answer

$$1.1 	imes 10$$^{-4}$$\ \mathrm{m/s}$$

Question 2

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

Accepted Answer

It is opposite to the flow of electrons.

Question 3

A resistor has a resistance of $$19.8\ \Omega at$$ $$15.0^\circ\mathrm{C}$$ and $$25.0\ \Omega at$$ $$85.0^\circ\mathrm{C}. $$What is the temperature coefficient of resistivity $$\alpha$$?

Accepted Answer

$$3.75 	imes 10$$^{-3}$$\ ^\circ\mathrm{C}^{-1}$$

Question 4

Which equation correctly gives the resistance $$R of a $$uniform cylindrical conductor of length $$L$$, cross-sectional area $$A$$, and resistivity $$\rho$$?

Accepted Answer

$$R = \rho \dfrac{L}{A}$$

Question 5

A $$15\ \mathrm{V}$$ potential difference is applied across a resistor, and the resistor dissipates $$327\ \mathrm{W} of $$power. What is the current through the resistor?

Accepted Answer

$$21.8\ \mathrm{A}$$

Question 6

Which of the following statements about superconductors is correct?

Accepted Answer

A superconductor has zero resistivity below its critical temperature.

Question 7

A voltmeter is used to measure the potential difference across a resistor in a circuit. How should it be connected, and why?

Accepted Answer

In parallel with the resistor, because it has a large internal resistance.

Question 8

Which of the following materials would be considered a good conductor based on its resistivity?

Accepted Answer

A material with a small value of $$\rho$$

Question 9

If the cross-sectional area of a wire is doubled while keeping its length and material the same, what happens to its resistance?

Accepted Answer

It is halved.

Question 10

A current of $$80.0\ \mathrm{mA}$$ flows through a wire for $$10.0$$ minutes. How many electrons pass through a cross-section of the wire in this time?

Accepted Answer

$$3.00 	imes 10$$^{20}$$ electrons

Question 11

Which of the following is the correct expression for the current density $$J in $$terms of the number density $$n$$, charge $$q$$, and drift velocity $$v_d$$?

Accepted Answer

$$J = nqv_d$$

Question 12

A material is said to be ohmic if which of the following relationships holds?

Accepted Answer

$$\Delta V \propto I$$

Question 13

A wire is connected to a battery, and a steady current flows. Which of the following best describes the motion of the conduction electrons?

Accepted Answer

They move with a small average drift velocity opposite to the current.

Question 14

Which of the following equations gives the power dissipated by a resistor in terms of current $$I$$ and resistance $$R$$?

Accepted Answer

$$P = I^2$ R$$

Question 15

A sample of mercury is cooled below its critical temperature of $$4.2\ \mathrm{K}. $$What happens to its resistance?

Accepted Answer

It drops abruptly to zero.

Question 16

Which of the following best explains why the signal in a metal wire propagates rapidly even though the drift speed of electrons is very slow?

Accepted Answer

As one electron enters, another leaves almost immediately due to repulsion, transmitting the signal quickly.

Question 17

Which of the following is the correct relationship for the temperature dependence of resistivity?

Accepted Answer

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

Question 18

A circuit contains a resistor and an ammeter. How should the ammeter be connected, and why?

Accepted Answer

In series with the resistor, because it has a low internal resistance.

Question 19

A resistor is found to have a nonlinear $$V vs$$. $$I$$ graph. What does this indicate about the resistor?

Accepted Answer

It is non-ohmic.

Question 20

Which of the following is a correct unit for electrical resistance?

Accepted Answer

$$\Omega = \mathrm{V/A}$$

Current, Resistance, and Resistivity: Study Notes for PHY 131

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