Two conductors have the same resistance at `0^@C` but their temperature coefficient of resistanc are `alpha_1 and alpha_2`. The respective temperature coefficients of their series and parallel combinations are nearly

Options

A. `(alpha_(1)+alpha_(2))/(2),alpha_(1)+alpha_(2)`
B. `alpha_(1)+alpha_(2),(alpha_(1)+alpha_(2))/(2)`
C. `alpha_(1)+alpha_(2),(alpha_(1)alpha_(2))/(alpha_(1)+alpha_(2))`
D. `(alpha_(1)+alpha_(2))/(2),(alpha_(1)+alpha_(2))/(2)`

Answer

D

Explanation

`R_(1)=R_(0)(1+alpha_(1)(Deltat)),R_(2)=R_(0)(1+alpha_(2)(Deltat))`
Series `R=R_(1)+R_(2)`, parallel `(1)/(R)=(1)/(R_(1))+(1)/(R_(2))`