First slide

Temperature dependence

Question

The V – I graph for a conductor at temperature $T_{1} and T_{2}$ are as shown in figure. Then ( $T_{2} - T_{1}$ ) is equal to [ $α$ = temperature coefficient of resistivity]

Moderate

A

$\frac{2}{α}$
B

$\frac{4}{α}$
C

$\frac{8}{α}$
D

$\frac{1}{α}$

Solution

According to Ohm’s Law, V = R.I. It means that ‘R’ is the slope of V – I graph.
$∴ R_{1} = tanθ and ∴ R_{2} = R_{1} [1 + α (T_{2} - T_{1})] ∴ cotθ = tanθ [1 + α (T_{2} - T_{1})] \Rightarrow α (T_{2} - T_{1}) = (\frac{cotθ}{tanθ} - 1) \Rightarrow (T_{2} - T_{1}) = \frac{1}{α} . \frac{\cos 2 θ}{\sin^{2} θ} = \frac{1}{α} \frac{\cos 60^{0}}{\sin^{2} 30^{0}} = \frac{2}{α}$

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