Two resistances R1 and R2 are made of different materials- The temperature coefficient of the material of R1 is - and that of material of R2 is - The material of R1 and R2 will not change with temperature if R1-R2 equal to

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Byju's Answer

Standard XII

Physics

Dependence of Resistance on Temperature

Two resistanc...

Question

Two resistances $R_{1}$ and $R_{2}$ are made of different materials. The temperature coefficient of the material of $R_{1}$ is $α$ and that of material of $R_{2}$ is $- β$ . The material of $R_{1}$ and $R_{2}$ will not change with temperature if $\frac{R_{1}}{R_{2}}$ equal to

\frac{α}{β}

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\frac{α + β}{α - β}

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\frac{α^{2} + β^{2}}{2 α β}

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\frac{β}{α}

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Solution

The correct option is D $\frac{β}{α}$
Here, $R_{1} + R_{2} =$ constant
Thus, $R_{1}$ will increase, $R_{2}$ will decrease.
So, $R_{1} α Δ T - R_{2} β Δ T = 0$
$\Rightarrow \frac{R_{1}}{R_{2}} = \frac{β}{α}$

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