Q: A circuit contains a $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor in parallel. What is the equivalent resistance?

$$R_{\text{eq}} = \frac{10 \times 20}{10 + 20} = 6.67\ \Omega$$

Q: A wire carries a current of $$3\ \mathrm{A}$$ and has a cross-sectional area of $$2 \times 10$$^{-6}$$\ \mathrm{m}^2. $$What is the current density $$J$$?

$$J = \frac{3}{2 \times 10$$^{-6}$$} = 1.5 \times 10$$^{6}$$\ \mathrm{A/m}^2$$

Question 1

Which of the following best describes Ohm's Law for a conductor?

Accepted Answer

The current through a conductor is proportional to the voltage across it: $$I = \frac{V}{R}$$

Question 2

A wire has a resistance $$R$$ and a length $$L. If $$the wire is stretched to double its original length without changing its volume, what happens to its resistance?

Accepted Answer

The resistance increases by a factor of four.

Question 3

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

Accepted Answer

$$I = n e A v_d$$

Question 4

A resistor is connected to a $$12\ \mathrm{V}$$ battery and the current through it is $$2\ \mathrm{A}. $$What is the power dissipated by the resistor?

Accepted Answer

$$P = 24\ \mathrm{W}$$

Question 5

Which of the following is the correct expression for the resistivity $$\rho of a $$material?

Accepted Answer

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

Question 6

If the cross-sectional area $$A of a $$wire is halved while keeping its length $$L$$ and material constant, what happens to its resistance $$R$$?

Accepted Answer

The resistance doubles.

Question 7

A copper wire has a number density of free electrons $$n$$, charge of electron $$e$$, cross-sectional area $$A$$, and drift velocity $$v_d. $$Which formula gives the current $$I in $$the wire?

Accepted Answer

$$I = n e A v_d$$

Question 8

Which of the following statements about resistors in series is correct?

Accepted Answer

The total resistance is the sum of the individual resistances: $$R_{	ext{total}} = R_1$ + R_2$ + \ldots$$

Question 9

A circuit contains a $$10\ \Omega$$ resistor and a $$20\ \Omega$$ resistor in parallel. What is the equivalent resistance?

Accepted Answer

$$R_{	ext{eq}} = \frac{10 	imes 20}{10 + 20} = 6.67\ \Omega$$

Question 10

Which of the following best describes the physical meaning of current density $$J$$?

Accepted Answer

Current per unit area: $$J = \frac{I}{A}$$

Question 11

A $$5\ \Omega$$ resistor is connected in series with a $$10\ \Omega$$ resistor to a $$30\ \mathrm{V}$$ battery. What is the current in the circuit?

Accepted Answer

$$I = \frac{30}{15} = 2\ \mathrm{A}$$

Question 12

Which of the following is the correct formula for the conductivity $$\sigma of a $$material?

Accepted Answer

$$\sigma = \frac{1}{\rho}$$

Question 13

A battery supplies a constant voltage $$V to a $$resistor $$R. If $$the resistance is increased, what happens to the current?

Accepted Answer

The current decreases.

Question 14

Which of the following is the correct expression for the power $$P$$ dissipated in a resistor?

Accepted Answer

$$P = I^2$ R$$

Question 15

A wire of length $$L$$ and area $$A$$ has resistance $$R. If $$both the length and area are doubled, what happens to the resistance?

Accepted Answer

The resistance remains the same.

Question 16

Which of the following is true about the drift velocity $$v_d in a $$conductor when the current increases?

Accepted Answer

The drift velocity increases.

Question 17

A $$100\ \Omega$$ resistor is rated for $$2\ \mathrm{W}$$ maximum power. What is the maximum safe current that can pass through it?

Accepted Answer

$$I = \sqrt{\frac{P}{R}} = \sqrt{\frac{2}{100}} = 0.14\ \mathrm{A}$$

Question 18

Which of the following is the correct formula for the resistivity $$\rho in $$terms of the electric field $$E$$ and current density $$J$$?

Accepted Answer

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

Question 19

A wire carries a current of $$3\ \mathrm{A}$$ and has a cross-sectional area of $$2 	imes 10$$^{-6}$$\ \mathrm{m}^2. $$What is the current density $$J$$?

Accepted Answer

$$J = \frac{3}{2 	imes 10$$^{-6}$$} = 1.5 	imes 10$$^{6}$$\ \mathrm{A/m}^2$$

Electric Current, Ohm's Law, and Electrical Circuits

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