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Question

A copper wire carries \( 2.72 \, \text{A} \) with a drift speed of \( 8 \times 10^{-5} \, \text{m/s}
\). If \( n = 8.5 \times 10^{28} \, \text{m}^{-3} \) and \( e = 1.6 \times 10^{-19} \, \text{C} \), what
is the cross-sectional area?

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Explanation

**Potentiometer** measures potential difference without drawing current, using null deflection, principle V ∝ l, l balance length, accurate because no I r drop. Potential drop across resistor V = I R arises because electric field does work on charges, energy converted to heat, maintaining E = -dV/dx along wire. Drift speed: v_d = (I/n e A) . Rearrange: A = (I/n e v_d) . Substitute: A = (2.72/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 8 × 10⁻⁵) . Calculate: A = (2.72/1.088 × 10⁵) ≈ 2.5 × 10⁻⁵ m² . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT],

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