Question

At the temperature `0^(@)C` the electron of conductor `B` is `n` times that of condoctor A temperaturte coefficient of resistance are equal to `alpha_(2) and alpha_(1)` respectively find the resistance and A temperaturte coefficient of resistance of a segment of these two condustore when they are conected in series

Answer 1

Let `R_(0)` be the resistance of coefficient `A` at `0^(@)C` resistance of conductor `B` at `0^(@)C = nR_(0)`
If `R_(t_1),R_(t_2)` are the resistance of coefficient A and B at at `t^(@)C` then `R_(t_1)=R_(0)(1 + alpha_(2) t) and R_(t_2)= nR_(0)(1 + alpha_(2) t)`
If `R_(g)` is the resistance at `t^(@)C` then they are commected in series then
`R_(s) =R_(t_1)+ R_(t_2)( 1+ alpha_(1) t) +nR_(0) (1 + alpha_(2) t)= R_(0) (1+ n) + R_(0) (alpha_(1) +n alpha_(2))t`
`= R_(0) (1 + n) [ 1+ ((alpha_(1) +n alpha_(2)))/(( 1+ n))t]`....(i)
If `R_(0)` is the resistance of combination of two condactor at `0^(@)C` and `alpha ` is the temperature coefficient of these two conducators in series then `R_(s) = R_(0) (1 + alpha t)` ....(ii)
Comparing (i) and (ii) we have `R_(0) (1 + n) and alpha = ((alpha_(1) + n alpha_(2))/(1 + n))`