Q: A copper wire of length 2 m and cross-sectional area $$1 \times 10$$^{-6}$$ \ \mathrm{m}^2$$ carries a current of 3 A. If the number density of free electrons in copper is $$8.5 \times 10$$^{28}$$ \ \mathrm{m}^{-3}$$, what is the drift velocity of electrons in the wire? (Charge of electron $$e = 1.6 \times 10$$^{-19}$$ \ \mathrm{C})$$

$$2.2 \times 10$$^{-4}$$ \ \mathrm{m/s}$$

Q: A wire carries a current of $$2 \ \mathrm{A}. If $$the number density of free electrons is $$5 \times 10$$^{28}$$ \ \mathrm{m}^{-3}$$, the cross-sectional area is $$2 \times 10$$^{-6}$$ \ \mathrm{m}^2$$, and the charge of an electron is $$1.6 \times 10$$^{-19}$$ \ \mathrm{C}$$, what is the drift velocity?

$$1.25 \times 10$$^{-4}$$ \ \mathrm{m/s}$$

Q: A current of $$5 \ \mathrm{A}$$ flows through a wire with a cross-sectional area of $$1 \times 10$$^{-6}$$ \ \mathrm{m}^2. $$What is the current density?

$$5 \times 10$$^{6}$$ \ \mathrm{A/m}^2$$

Question 1

A copper wire of length 2 m and cross-sectional area $$1 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$ carries a current of 3 A. If the number density of free electrons in copper is $$8.5 	imes 10$$^{28}$$ \ \mathrm{m}^{-3}$$, what is the drift velocity of electrons in the wire? (Charge of electron $$e = 1.6 	imes 10$$^{-19}$$ \ \mathrm{C})$$

Accepted Answer

$$2.2 	imes 10$$^{-4}$$ \ \mathrm{m/s}$$

Question 2

Which of the following statements best describes the relationship between resistance and temperature for most metals?

Accepted Answer

Resistance increases as temperature increases.

Question 3

A wire has a resistance $$R. If $$its length is doubled and its cross-sectional area is halved, what will be its new resistance?

Accepted Answer

$$4R$$

Question 4

Which of the following equations correctly relates current density $$J to $$drift velocity $$v_d$$?

Accepted Answer

$$J = n e v_d$$

Question 5

A student claims that doubling the voltage across an Ohmic resistor will double the current. Is this claim correct? Why?

Accepted Answer

Yes, because Ohm's Law states $$V = I R$$, so $$I is $$directly proportional to $$V.$$

Question 6

A cylindrical aluminum wire has a resistance of $$5 \ \Omega. If $$another wire made of the same material has twice the length and three times the cross-sectional area, what is its resistance?

Accepted Answer

$$3.33 \ \Omega$$

Question 7

Which of the following best explains why thick wires are used in high-current applications?

Accepted Answer

Thicker wires have lower resistance, allowing more current to flow with less energy loss.

Question 8

A current of $$0.5 \ \mathrm{A}$$ flows through a conductor for 10 minutes. How much charge passes through the conductor in this time?

Accepted Answer

$$300 \ \mathrm{C}$$

Question 9

Which of the following materials is most likely to obey Ohm's Law?

Accepted Answer

A metallic resistor at constant temperature

Question 10

If the current density in a wire is $$2 \ \mathrm{A/m}^2$$ and the cross-sectional area is $$0.5 \ \mathrm{m}^2$$, what is the total current flowing through the wire?

Accepted Answer

$$1 \ \mathrm{A}$$

Question 11

A wire of resistivity $$\rho$$ and length $$L is $$stretched to double its original length without changing its volume. What happens to its resistance?

Accepted Answer

It becomes four times its original value.

Question 12

Which of the following is the correct SI unit for current density?

Accepted Answer

$$\mathrm{A/m}^2$$

Question 13

A wire carries a current of $$2 \ \mathrm{A}. If $$the number density of free electrons is $$5 	imes 10$$^{28}$$ \ \mathrm{m}^{-3}$$, the cross-sectional area is $$2 	imes 10$$^{-6}$$ \ \mathrm{m}^2$$, and the charge of an electron is $$1.6 	imes 10$$^{-19}$$ \ \mathrm{C}$$, what is the drift velocity?

Accepted Answer

$$1.25 	imes 10$$^{-4}$$ \ \mathrm{m/s}$$

Question 14

Which of the following best describes the physical meaning of drift velocity?

Accepted Answer

The average velocity of electrons in the direction of the electric field.

Question 15

A resistor is made from a material with resistivity $$1.7 	imes 10$$^{-8}$$ \ \Omega \cdot \mathrm{m}$$, length $$0.5 \ \mathrm{m}$$, and cross-sectional area $$2 	imes 10$$^{-6}$$ \ \mathrm{m}^2. $$What is its resistance?

Accepted Answer

$$0.00425 \ \Omega$$

Question 16

Which of the following changes will decrease the resistance of a metallic wire?

Accepted Answer

Using a material with lower resistivity

Question 17

A current of $$5 \ \mathrm{A}$$ flows through a wire with a cross-sectional area of $$1 	imes 10$$^{-6}$$ \ \mathrm{m}^2. $$What is the current density?

Accepted Answer

$$5 	imes 10$$^{6}$$ \ \mathrm{A/m}^2$$

Question 18

A household extension cord is made of copper and is used to power a high-wattage appliance. Which property of the cord is most important to minimize energy loss?

Accepted Answer

Large cross-sectional area

Question 19

If a conductor obeys Ohm's Law, what would a graph of voltage ($$V) $$versus current ($$I) $$look like?

Accepted Answer

A straight line passing through the origin

Question 20

A wire with resistance $$10 \ \Omega is $$connected to a $$20 \ \mathrm{V}$$ battery. What is the current through the wire?

Accepted Answer

$$2 \ \mathrm{A}$$

Electric Current and Resistance: Principles and Applications

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