Question

When a metal rod is heated, not only its resistance but also its length and cross‐sectional area change. The relation R = ρL / A suggests that all three factors should be taken into account in measuring ρ at various temperatures. If the temperature changes by 1.10^oC, what percentage changes in (a) L, (b) A, and (c) R occur for a copper conductor? The coefficient of linear expansion is 1.70 × 10^-5 K^-1. Coefficient of resistivity for copper is 4.30 × 10^-3 K^-1.

Answer 1

A)

(dL/L) x 100 = (L a dt) /L = (a dt) x 100 = (1.7 x 10^-5) 1.1 x 100 = 1.87 x 10^-3 %

B)

(dA/A) x 100 = 2 x 1.87 x 10^-3 = 3.74 x 10^-3 %

C)

(dR/R) x 100 = 4.3 x 10^-3 x 1.1 x 100 = 0.473 %

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