Current from electron drift velocity

Steps:

• Total charge Q = N × e = 5.1 × 10^{20} × 1.6 × 10^{-19} C = 81.6 C (using typical problem value for free electrons).
• Drift speed v_d = 0.4 × 10^{-3} m/s; length L = 12 cm = 0.12 m.
• Transit time t = L / v_d = 0.12 / (0.4 × 10^{-3}) = 300 s.
• Current I = Q / t = 81.6 / 300 = 0.272 A ≈ 0.27 A.

Why C is correct:

• Ohm's law in microscopic form I = n e A v_d simplifies to I = N e v_d / L since n A L = N, yielding 0.27 A.

Why the others are wrong:

• A. 0.002 A results from mistakenly using L = 1.2 m, increasing t by factor of 10.
• B. 0.009 A arises from underestimating Q by factor of ~3 or misapplying v_d.
• D. 0.38 A comes from overestimating v_d by ~40% or using incorrect e value.

Final answer: C