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Standard XII

Physics

Dependence of Resistance on Temperature

Two resistanc...

Question

Two resistance at $0^{\circ} C$ with temperature coefficient of resistance $α_{1}$ and $α_{2}$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

α_{1} + α_{2}

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\frac{α_{1} α_{2}}{α_{1} + α_{2}}

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\frac{α_{1} - α_{2}}{2}

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\frac{α_{1} + α_{2}}{2}

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Solution

The correct option is D $\frac{α_{1} + α_{2}}{2}$
$R_{1} = R_{0} (1 + α_{1} t) + R_{0} (1 + α_{2} t)$
$= 2 R_{0} (1 + \frac{α_{1} + α_{2}}{2} t)$
Comparing with $R = R_{0} (1 + α t)$
$α = \frac{α_{1} + α_{2}}{2}$ .

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