First slide

Temperature dependence

Question

The temperature coefficient of resistance of conductor varies as $α (T) = 3 T^{2} + 2 T$ .If $R_{0}$ is resistance at T = 0 and R is resistance at T, then

Moderate

A

$R = R_{0} (6 T + 2)$
B

$R = 2 R_{o} (3 + 2 T)$
C

$R = R_{0} (1 + T^{2} + T^{3})$
D

$R = R 0 (1 - T + T^{2} + 2)$

Solution

$α (T) = \frac{1}{R_{0}} \frac{d R}{d T}$ $\Rightarrow$ $(3 T^{2} + 2 T) = \frac{1}{R_{0}} \frac{d R}{d T}$ $\Rightarrow$ $\int_{R_{0}}^{R} d R = R_{0} [3 \int_{0}^{T} T^{2} d T + 2 \int_{0}^{T} T d T]$
$\Rightarrow R = R_{0} [1 + T^{2} + T^{3}]$

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