In the post office box circuit, $10 Ω$ plug is taken out in arm AB and $100 Ω$ plug is taken out in arm BC. If the unknown resistor is kept in melting ice chamber, $600 Ω$ resistance is required in arm AD for zero deflection in galvanometer. Now, if the unknown resistor is kept at $100 ° C$ (steam chamber), $630 Ω$ resistance is required in arm AD for zero deflection. Temperature coefficient of resistance of the unknown wire is found to be $p \times 10^{- 4} / C °$ . Find the value of p ?

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answer is 5.

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Detailed Solution

$\begin{array}{l} \frac{P}{Q} = \frac{R}{X} \\ \Rightarrow \frac{10}{100} = \frac{600}{X} \\ \Rightarrow X = 6000 Ω \\ For second case \\ \frac{P}{Q} = \frac{R}{X} \\ \Rightarrow \frac{10}{100} = \frac{630}{X} \\ \Rightarrow X = 6300 Ω \\ R_{f} = R_{0} (1 + α Δ T) \\ \Rightarrow 6300 = 6000 (1 + α (100)) \\ \Rightarrow α = 5 \times 10^{- 4} / C^{°} \end{array}$