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Question

A nichrome wire has a resistance of \( 70 \, \Omega \) at \( 30^\circ \text{C} \) and \( \alpha = 1.7
\times 10^{-4} \, ^\circ\text{C}^{-1} \). What is its resistance at \( 270^\circ \text{C} \)?

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Explanation

**Ohm's law deviation** at high fields occurs when τ or n vary with E, resistivity ρ = m/(n e² τ) changes, non-ohmic behaviour seen in semiconductors, electrolytes. At moderate fields, linear V-I holds, slope = R. Use: R_t = R₀ [1 + α (T - T₀)] . Substitute: R_t = 70 [1 + 1.7 × 10⁻⁴ (270 - 30)] . Calculate: R_t = 70 [1 + 1.7 × 10⁻⁴ × 240] = 70 [1 + 0.0408] = 70 × 1.0408 = 72.86 Ω . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V =

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