Two resistance R 1 and R 2 are made of different materials- The temperature coefficient of the material of R 1 is - and that of the material of R 2 is - The resistance of the series combination of R 1 and R 2 does not change with temperature- then the ratio of resistances of the two wires at 0- C will be-A- -B- -2-2-C- -2 -D- -

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Resistance and Resistors

Two resistanc...

Question

Two resistance $R_{1}$ and $R_{2}$ are made of different materials. The temperature coefficient of the material of $R_{1}$ is $α$ and that of the material of $R_{2}$ is $β$ . The resistance of the series combination of $R_{2}$ and $R_{1}$ does not change with temperature, then the ratio of resistances of the two wires at $0^{o}$ will be:

\frac{2 α}{β}

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\frac{α + β}{α - β}

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\frac{α^{2} + β^{2}}{α β}

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\frac{β}{α}

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Solution

The correct option is D $\frac{β}{α}$
Resistance of wire as temperature changes is
$R_{1} = R_{01} (1 + α Δ T)$
$R_{2} = R_{02} (1 - β Δ T)$
Both are connected in series;
$R_{s e r i e s} =$ $R_{01} (1 + α Δ T) +$ $R_{02} (1 - β Δ T)$
$R_{s e r i e s} =$ is independent of temperature, si cofficient of temperature will be eqaul to zero,
$R_{01} α - R_{02} β = 0 ⟹ \frac{R_{01}}{R_{02}} = \frac{β}{α}$

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