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]`.

Explanation

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`.