Q: A copper wire has a cross-sectional area of $$8.17 \times 10$$^{-7}$$\ \mathrm{m}^2$$ and carries a current of $$1.67\ \mathrm{A}. $$What is the current density $$J in $$the wire?

$$J = 2.04 \times 10$$^{6}$$\ \mathrm{A/m}^2$$

Question 1

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

Accepted Answer

It is opposite to the direction of electron flow.

Question 2

A copper wire has a cross-sectional area of $$8.17 	imes 10$$^{-7}$$\ \mathrm{m}^2$$ and carries a current of $$1.67\ \mathrm{A}. $$What is the current density $$J in $$the wire?

Accepted Answer

$$J = 2.04 	imes 10$$^{6}$$\ \mathrm{A/m}^2$$

Question 3

Which equation correctly relates the resistance $$R of a $$wire to its resistivity $$\rho$$, length $$L$$, and cross-sectional area $$A$$?

Accepted Answer

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

Question 4

If the resistance of a copper wire at $$20^\circ\mathrm{C} is$$ $$1.05\ \Omega$$, what is its resistance at $$100^\circ\mathrm{C}$$? (Given $$\alpha = 0.00393\ \mathrm{C}^{-1}$$ for copper)

Accepted Answer

$$R = 1.49\ \Omega$$

Question 5

Which material listed below has the lowest resistivity at room temperature?

Accepted Answer

Copper

Question 6

What happens to the resistivity of a typical metal as temperature increases?

Accepted Answer

Resistivity increases linearly with temperature.

Question 7

A wire of length $$L$$ and cross-sectional area $$A is $$made of a material with resistivity $$\rho. If $$the wire is stretched so that its length doubles and its volume remains constant, what happens to its resistance?

Accepted Answer

The resistance increases by a factor of 4.

Question 8

Which of the following statements about superconductors is correct?

Accepted Answer

Their resistivity drops abruptly to zero below a critical temperature.

Question 9

A solution of sodium chloride conducts electricity. What is the total current in the solution?

Accepted Answer

It is the sum of the currents due to both sodium and chloride ions.

Question 10

Which equation gives the drift speed $$v_d of $$charge carriers in a conductor?

Accepted Answer

$$v_d = \dfrac{I}{nqA}$$

Question 11

A copper wire of length $$50.0\ \mathrm{m}$$ and cross-sectional area $$8.17 	imes 10$$^{-7}$$\ \mathrm{m}^2$$ carries a current of $$1.67\ \mathrm{A}. $$Given $$ho = 1.72 	imes 10$$^{-8}$$\ \Omega\cdot\mathrm{m}$$, what is the potential difference across the wire?

Accepted Answer

$$V = 1.76\ \mathrm{V}$$

Question 12

Which of the following is true for an ohmic resistor?

Accepted Answer

The current is directly proportional to the voltage at a constant temperature.

Question 13

A semiconductor diode is an example of a nonohmic resistor. Which statement best describes its current-voltage relationship?

Accepted Answer

Current increases nonlinearly with voltage in the forward direction.

Question 14

Which formula correctly expresses the temperature dependence of resistance for a metal?

Accepted Answer

$$R(T) = R_0$ [1 + \alpha (T - T_0$)]$$

Question 15

Which of the following best explains why circuit boards can have copper traces close together without short-circuiting?

Accepted Answer

The insulating board has a very high resistivity, preventing current flow between traces.

Question 16

If a thermistor is used as a thermometer, which property of semiconductors does it exploit?

Accepted Answer

Resistivity decreases with increasing temperature.

Question 17

Which equation defines the vector current density $$\vec{J} in $$terms of charge carrier concentration $$n$$, charge $$q$$, and drift velocity $$\vec{v}_d$$?

Accepted Answer

$$\vec{J} = n q \vec{v}_d$$

Question 18

A wire has a resistance $$R at $$temperature $$T_0. If $$the temperature increases by $$\Delta T$$, and the temperature coefficient of resistivity is $$\alpha$$, what is the new resistance?

Accepted Answer

$$R_{new} = R [1 + \alpha \Delta T]$$

Question 19

Which of the following is the correct definition of resistivity $$\rho$$?

Accepted Answer

$$\rho = \dfrac{E}{J}$$

Current, Resistance, and Electromotive Force (EMF)

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