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Resistance

If R 1 and R ...

Question

If $R_{1}$ and $R_{2}$ are the resistance of a conductor at two temperatures $t_{1}^{0} C$ and $t_{2}^{0} C$ respectively, show that the temperature coefficient of resistance, $α = \frac{R_{2} - R_{1}}{R_{1} t_{2} - R_{2} t_{1}}$

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Solution

Given $R_{1}$ and $R_{2}$ are the resistance of a conductor at two temperatures $t_{1}^{0} C$ and $t_{1}^{0} C$ respectively.

We know that the resistance of a conductor varies with temperature as,

$R_{t} = R_{0} (1 + t)$

$R_{0} \to$ resistance at $0^{\circ} C, R_{t} t o$ resistance at $t^{\circ} C \propto$

$\propto\to$ temperature coefficient of resistance

We have $R_{1} = R_{0} (1 + t_{1}) f o r t_{1}^{\circ} C$

And $R_{2} = R_{0} (1 + t_{2}) f o r t_{2}^{\circ} C$

Taking ratio, $= \frac{R_{2}}{R_{1}} = \frac{R_{0} (1 + \propto t_{2})}{R_{0} (1_{\propto} t_{1})}$

We get, $R_{2} + R_{2} \propto t_{1} = R_{1} + R_{1} \propto t_{2}$

(Or) $\propto= \frac{R_{2} - R_{1}}{R_{1} t_{2} - R_{2} t_{1}}$

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