Question

A uniform copper wire of length 1m and cross-sectional area \(5 \times 10^{-7} \, \text{m}^2\) carries a current of 1A. Assuming that there are \(8 \times 10^{28} \, \text{free electrons/m}^3\) in copper, how long will an electron take to drift from one end of the wire to the other?

• A. \( 0.8 \times 10^{-3} \) s
• B. \( 3.2 \times 10^{-3} \) s
• C. \( 1.6 \times 10^{-3} \) s
• D. \( 6.4 \times 10^{-3} \) s

Hint:

Drift velocity depends on current, cross-sectional area, and the number of free electrons in the conductor.

Answer 1

The Correct Option is D

Step 1: Drift velocity equation.
The drift velocity \( v_d \) is given by the formula: \[ v_d = \frac{I}{nA e} \] where \( I \) is the current, \( n \) is the number of electrons per unit volume, \( A \) is the cross-sectional area, and \( e \) is the charge of an electron.

Step 2: Calculate drift time.
The drift time \( t \) is the distance divided by the drift velocity, i.e., \[ t = \frac{L}{v_d} \] where \( L = 1 \, \text{m} \). After substituting the given values, we calculate \( t \). Thus, the correct answer is option (D).

Final Answer: \[ \boxed{6.4 \times 10^{-3} \, \text{s}} \]