Two wires of resistance `R_(1)` and `R_(2)` have temperature coefficient of resistance `alpha_(1)` and `alpha_(2)` respectively. These are joined in series. The effective temperature coefficient of resistance is

Options

A. `(alpha_(1) + alpha_(2))/2`
B. `sqrt(alpha_(1) alpha_(2))`
C. `(alpha_(1)R_(1) + alpha_(2)R_(2))/(R_(1) + R_(2))`
D. `sqrt((R_(1)R_(2)alpha_(1)alpha_(2)))/sqrt(R_(1)^(2) + R_(2))`

Answer

A

Explanation

`R_(1) =R_(0)(1 + alpha_(1)DeltaT)`
`R_(2) = R_(0) (1 + alpha_(2)DeltaT)`
`R = R_(1) +R_(2) =R_(0)[2 + (alpha_(1) + alpha_(2))DeltaT]`
`rArr R =2R_(0)[1 + (alpha_(1) + alpha_(2))/2.DeltaT]`
`alpha = (alpha_(1) + alpha_(2))/2`