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×$$10$$−$$4/C$$°. Find the value of p ?

Question

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×$$10$$−$$4/C$$°. Find the value of p ?

Infinity Learn · Accepted Answer

$$PQ=RX$$⇒$$10100=600X$$⇒$$X=6000$$Ω For second case $$PQ=RX$$⇒$$10100=630X$$⇒$$X=6300$$Ω$$Rf=R0(1+$$αΔ$$T)$$⇒$$6300=6000(1+$$α(100))⇒α$$=5$$×$$10$$−$$4/C$$°

Detailed Solution

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