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

$$v_d = 7.4 \times 10$$^{-5}$$ \ \mathrm{m/s}$$

Question 1

Which of the following best defines electric current in a wire?

Accepted Answer

The rate of charge passing through a cross-sectional area of the wire.

Question 2

A capacitor is discharged through a wire, and the connecting wire gets warm. What is the most direct explanation for this observation?

Accepted Answer

The moving charges (current) in the wire cause collisions with atoms, producing heat.

Question 3

Which of the following equations correctly expresses the current $$I$$ through a wire in terms of the rate of change of charge $$Q$$?

Accepted Answer

$$I = \frac{dQ}{dt}$$

Question 4

The SI unit of electric current, the ampere (A), can be expressed in terms of which fundamental units?

Accepted Answer

$$\mathrm{A} = \frac{\mathrm{C}}{\mathrm{s}}$$

Question 5

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

Accepted Answer

$$v_d = 7.4 	imes 10$$^{-5}$$ \ \mathrm{m/s}$$

Question 6

If you connect the plates of a charged capacitor through a light bulb and observe the bulb lights up briefly, what does this demonstrate?

Accepted Answer

A current flows as the capacitor discharges, providing energy to the bulb.

Question 7

Which of the following statements about the motion of electrons in a metal wire carrying current is correct?

Accepted Answer

Electrons undergo random motion but have a small net drift velocity opposite to the current.

Question 8

A battery is rated at $$2 \ \mathrm{Ah}. $$How much charge, in coulombs, can it deliver before being exhausted?

Accepted Answer

$$7200 \ \mathrm{C}$$

Question 9

Which of the following best describes the function of a Galvanic cell (battery) in an electric circuit?

Accepted Answer

It provides a potential difference by moving ions and thus drives current through the circuit.

Question 10

If the current through a wire is $$I = 3 \ \mathrm{A}$$, how much charge passes through a cross-section of the wire in $$4 \ \mathrm{s}$$?

Accepted Answer

$$12 \ \mathrm{C}$$

Question 11

A rechargeable battery provides a constant current of $$0.5 \ \mathrm{A}$$ for $$4$$ hours before being exhausted. What is the total charge delivered?

Accepted Answer

$$7200 \ \mathrm{C}$$

Question 12

Which of the following is a correct statement about the direction of conventional current in a metal wire?

Accepted Answer

It is opposite to the direction of electron flow.

Question 13

If the number density of conduction electrons in a metal is doubled, what happens to the average drift velocity for a given current?

Accepted Answer

It is halved.

Question 14

Which of the following best explains why the average drift velocity of electrons in a wire is so much smaller than the random thermal velocity?

Accepted Answer

The electric field is very weak compared to the forces causing random motion.

Question 15

A student claims that increasing the temperature of a wire will always increase the current for a given voltage. Is this correct? Why or why not?

Accepted Answer

No, because increasing temperature increases resistance, which can decrease current.

Question 16

Which of the following is the correct formula for the current $$I in $$terms of the number density $$n$$, charge $$e$$, cross-sectional area $$A$$, and drift velocity $$v_d$$?

Accepted Answer

$$I = n e A v_d$$

Question 17

A wire carries a steady current. Which of the following statements is true about the charge entering and leaving the wire in a given time interval?

Accepted Answer

The amount of charge entering equals the amount leaving.

Question 18

Which of the following is a real-world application of the concept of electric current as described in the study material?

Accepted Answer

The operation of a battery-powered flashlight.

Question 19

A $$1 \ \mathrm{mm}^2$$ copper wire carries a current of $$2 \ \mathrm{A}. If $$the drift velocity of electrons is $$1.5 	imes 10$$^{-4}$$ \ \mathrm{m/s}$$, what is the number density $$n of $$conduction electrons? (Charge of electron $$e = 1.6 	imes 10$$^{-19}$$ \ \mathrm{C})$$

Accepted Answer

$$n = 8.3 	imes 10$$^{28}$$ \ \mathrm{m}^{-3}$$

Question 20

Which of the following observations would NOT indicate the presence of an electric current in a wire?

Accepted Answer

The wire remains at room temperature and no magnetic effects are observed.

Electric Current: Concepts, Measurement, and Sources

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