A carbon and an aluminimum wire are connected in series.If the combination has resistance of `27` ohm at `0^(@)C`,what is the resistance of each wire at `0^(@)C` so that the resistance of the combination does not change with temperature ? `[alpha_(C ) = -0.5 xx 10^(-3)(.^@C)^(-1)` and `alpha_(A) = 4 xx 10^(-3)(.^@C)^-1]`.

A carbon and an aluminimum wire are connected in series.If the combina

1.	A carbon and an aluminimum wire are connected in series.If the combination has resistance of `27` ohm at `0^(@)C`,what is the resistance of each wire at `0^(@)C` so that the resistance of the combination does not change with temperature ? `[alpha_(C ) = -0.5 xx 10^(-3)(.^@C)^(-1)` and `alpha_(A) = 4 xx 10^(-3)(.^@C)^-1]`.
Answer» The equivalent resistance in series `R = R_(Cu) + R_(A 1)` =`(R_(Cu))_0[1 + alpha_(Cu) Delta theta] + (R_(A1))_0[1 + alpha_(A1) Delta theta]` =`(R_(Cu))_0 +(R_(A1))_0 + [(R_(Cu))_0 alpha_(Cu) + (R_(A1))_0 alpha_(A1)]Delta theta` `(R_(Cu))_0 + (R_(A1))_0 = 27` ...(i) `(R_(Cu))_0 alpha_(Cu) + (R_(A1))alpha_(A1) =0` `4 xx 10^-3(R_(Cu))_0 -0.5 xx 10^-3(R_(A1))_0 = 0` `(R_(A1))_0 = 8 (R_(Cu))_0` ....(ii) Solving `(R_(Cu))_0 = 3 Omega, (R_(A1))_0 = 24 Omega`.

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