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Question

A conductor has a resistivity of \( 8 \times 10^{-8} \, \Omega \text{m} \) and \( \alpha = 4 \times
10^{-3} \, ^\circ\text{C}^{-1} \) at \( 20^\circ \text{C} \). What is its resistivity at \( 70^\circ
\text{C} \)?

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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. Use: rho_t = rho₀ [1 + α (T - T₀)] . Substitute: rho_t = 8 × 10⁻⁸ [1 + 4 × 10⁻³ (70 - 20)] . Calculate: rho_t = 8 × 10⁻⁸ [1 + 0.2] = 8 × 10⁻⁸ × 1.2 = 9.6 × 10⁻⁸ Ω m . Applying I = n e A v_d, R

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