At `0^(@)C` the resistance of conductor of a conductor `B` is `n` times that of condoctor A temperature coefficient of resistance for A and B are `alpha_(1) and alpha_(2)` respectively the temperature coefficient of resistance of a circiut segment constant A and B in series is
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Let `R_(0)` be the resistance of the conducor at `0^@C`. Then resistance of conductor B at `0^@C= n R_(0)`. Resistance of conductor A at `theta^@C`, `R_(1)=R_(0)(1+alpha_(1)theta)` Resistance of conductor B at `theta^@C`, `R_(2)=n R_(0)(1+alpha_(2)theta)` Thus the total resistance of the series combinatio at `theta^@C` is `R_(s)=R_(1)+R_(2)= R_(0)(1+alpha_(1)theta) + n R_(0)(1+alpha_(2)theta)` `= R_(0)[(1+n)+(alpha + n alpha_(2))theta]` `=(1+n)R_(0) [1+ (alpha_(1) + n alpha_(2))/(1+n) theta]` Comparing this relation with `R_(s)=R_(s0)[1+alpha_(s) theta]` We have resistance of series combination at `0^@C` `R_(s0)=(1+n)R_(0)` Tempeature coefficinet of resistance of the series combination is `alpha_(s) = (alpha_(1) _ n alpha_(2))/(1+n)`
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