Q: A copper wire has a length of 2.0 m and a cross-sectional area of $$1.0 \times 10$$^{-6}$$ \ \mathrm{m}^2. If $$the resistivity of copper is $$1.69 \times 10$$^{-8}$$ \ \Omega \cdot \mathrm{m}$$, what is the resistance of the wire?

$$3.38 \times 10$$^{-2}$$ \ \Omega$$

Q: The resistivity of a metal at $$20^\circ \mathrm{C} is$$ $$1.5 \times 10$$^{-8}$$\ \Omega \cdot \mathrm{m}$$ and its temperature coefficient $$\alpha is$$ $$4.0 \times 10$$^{-3}$$\ \mathrm{C}^{-1}. $$What is its resistivity at $$30^\circ \mathrm{C}$$?

$$1.56 \times 10$$^{-8}$$\ \Omega \cdot \mathrm{m}$$

Q: A $$100\ \mathrm{W}$$, $$120\ \mathrm{V}$$ lightbulb contains a tungsten filament of length $$7.0\ \mathrm{cm}$$ and resistivity $$9.0 \times 10$$^{-7}$$\ \Omega \cdot \mathrm{m}. $$What is the diameter of the filament?

$$2.6 \times 10$$^{-4}$$\ \mathrm{m}$$

Q: A liquid-filled pipe contains $$\mathrm{Ca}^{2+}$$ ions (each with charge $$+2e). $$The pipe has a radius of $$2.00\ \mathrm{mm}$$, current $$3.14 \times 10$$^{-4}$$\ \mathrm{A}$$, and drift velocity $$5.00 \times 10$$^{-4}$$\ \mathrm{m/s}. $$What is the density of $$\mathrm{Ca}^{2+}$$ ions in the pipe?

$$1.25 \times 10$$^{17}$$\ \mathrm{m}^{-3}$$

Question 1

A copper wire has a length of 2.0 m and a cross-sectional area of $$1.0 	imes 10$$^{-6}$$ \ \mathrm{m}^2. If $$the resistivity of copper is $$1.69 	imes 10$$^{-8}$$ \ \Omega \cdot \mathrm{m}$$, what is the resistance of the wire?

Accepted Answer

$$3.38 	imes 10$$^{-2}$$ \ \Omega$$

Question 2

A cylindrical wire has a radius $$r$$ and length $$\ell. If $$both $$r$$ and $$\ell$$ are doubled, how does the resistance of the wire change?

Accepted Answer

It remains the same.

Question 3

The current density $$J in a $$conductor is given by $$J = nqv_d. If $$the drift velocity $$v_d is $$doubled while all other factors remain constant, what happens to the current density?

Accepted Answer

It doubles.

Question 4

A battery with emf $$\mathcal{E} = 12\ \mathrm{V}$$ and internal resistance $$r = 2\ \Omega is $$connected to an external resistor $$R = 4\ \Omega. $$What is the current in the circuit?

Accepted Answer

$$2\ \mathrm{A}$$

Question 5

The resistivity of a metal at $$20^\circ \mathrm{C} is$$ $$1.5 	imes 10$$^{-8}$$\ \Omega \cdot \mathrm{m}$$ and its temperature coefficient $$\alpha is$$ $$4.0 	imes 10$$^{-3}$$\ \mathrm{C}^{-1}. $$What is its resistivity at $$30^\circ \mathrm{C}$$?

Accepted Answer

$$1.56 	imes 10$$^{-8}$$\ \Omega \cdot \mathrm{m}$$

Question 6

A $$100\ \mathrm{W}$$, $$120\ \mathrm{V}$$ lightbulb contains a tungsten filament of length $$7.0\ \mathrm{cm}$$ and resistivity $$9.0 	imes 10$$^{-7}$$\ \Omega \cdot \mathrm{m}. $$What is the diameter of the filament?

Accepted Answer

$$2.6 	imes 10$$^{-4}$$\ \mathrm{m}$$

Question 7

Which of the following statements is correct regarding two light bulbs, A (60 W) and B (100 W), both rated for $$110\ \mathrm{V}$$?

Accepted Answer

The 60 W bulb has a greater resistance and smaller current than the 100 W bulb.

Question 8

A wire has a resistance $$R at$$ $$20^\circ \mathrm{C}. If $$the temperature increases by $$50^\circ \mathrm{C}$$ and the temperature coefficient of resistance is $$0.004\ \mathrm{C}^{-1}$$, what is the new resistance?

Accepted Answer

$$R_{new} = R[1 + 0.2]$$

Question 9

A battery with emf $$\mathcal{E}$$ and internal resistance $$r is $$connected to a load resistance $$R. $$What is the terminal voltage $$V_{terminal}$$ across the battery?

Accepted Answer

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

Question 10

A cylindrical resistor $$R_2$$ has twice the length and half the radius of another resistor $$R_1$$, both made of the same material. What is the ratio $$R_2$$/$$R_1$$?

Accepted Answer

$$R_2$$/$$R_1 = 8$

Question 11

A voltmeter is connected in parallel with a resistor in a circuit. What does it measure?

Accepted Answer

The potential difference across the resistor.

Question 12

A $$5.7\ \mathrm{k}\Omega$$ resistor has a tolerance of $$\pm 10\%. $$What is the possible range of resistance values for this resistor?

Accepted Answer

$$5.13\ \mathrm{k}\Omega to$$ $$6.27\ \mathrm{k}\Omega$$

Question 13

Which material from the table has the lowest resistivity at $$20^\circ \mathrm{C}$$?

Accepted Answer

Silver

Question 14

A superconductor is characterized by which of the following properties below its critical temperature $$T_C$$?

Accepted Answer

Its resistance drops to virtually zero.

Question 15

A $$12\ \mathrm{V}$$ battery with internal resistance $$1\ \Omega is $$connected to a $$5\ \Omega$$ resistor. What is the power dissipated in the external resistor?

Accepted Answer

$$10\ \mathrm{W}$$

Question 16

In the circuit shown, two identical bulbs A and B are connected in series. If bulb B is removed and the circuit is completed, compared to the brightness of bulb A in the original circuit, bulb A in the new circuit is:

Accepted Answer

Brighter.

Question 17

A liquid-filled pipe contains $$\mathrm{Ca}^{2+}$$ ions (each with charge $$+2e). $$The pipe has a radius of $$2.00\ \mathrm{mm}$$, current $$3.14 	imes 10$$^{-4}$$\ \mathrm{A}$$, and drift velocity $$5.00 	imes 10$$^{-4}$$\ \mathrm{m/s}. $$What is the density of $$\mathrm{Ca}^{2+}$$ ions in the pipe?

Accepted Answer

$$1.25 	imes 10$$^{17}$$\ \mathrm{m}^{-3}$$

Question 18

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

Accepted Answer

It is the direction that positive charges would move.

Finding the Density of Charge Carriers in a Liquid-Filled Pipe

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