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)^( 2)))`

Answer

3

Explanation

`R_(1)=R_(1)(1+prop_(1) theta),R_(2)=R_(2)(1+prop_(2)theta)`
`R_("net")=R_(1)+R_(2)=R_(1)(1+prop_(1)theta)+R_(2)(1+prop_(2)theta)`
`=R_(1)+R_(2)+theta(R_(1)prop_(1)+R_(2)prop_(2))`
`=( R_(1)+R_(2))[1+(R_(1)prop_(1)+R_(2)prop_(2))/(R_(1)+R_(2))theta]`
compair this equation `R=R_(0)(1+prop_("net")theta)`
`therefore prop_("net")=(R_(1)prop_(1)+R_(2)prop_(2))/(R_(1)+R_(2))`