First slide

Resistivity of various materials

Question

If a copper wire is stretched to make its radius decrease by 0.1%, then percentage increase in resistance is approximately

Moderate

A

0.35%
B

0.4%
C

0.6%
D

0.2%

Solution

In case of stretching volume of wire is assumed to remain unchanged.
$∴ l A =$ constant and $L = \frac{c}{A}$
$∴ R = ρ . \frac{l}{A} = \frac{ρ . C}{A^{2}} = \frac{ρ . C}{{(A r^{2})}^{2}} = R \propto \frac{1}{r^{4}}$
$∴ \frac{Δ R}{R} = - 4 \frac{Δ r}{r} \times 100 %$
$= (- 4) \times (- 0.1 %) = + 0.4 %$

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