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

Answer

B

Explanation

Let `R_(0)` be the resistance of both conductors at `0^(@)C`.
Let `R_(1)andR_(2)` be their resistance at `T^(@)C`. Then
`R_(1)=R_(0)(1+alpha_(1)T)`
`R_(2)=R_(0)(1+alpha_(2)T)`
Let `R_(s)` is the resistance of the series combination of two conductors at `T^(@)C`. Then
`R_(s)=R_(1)+R_(2)`
`R_(s0)(1+alpha_(s)T)=R_(0)(1+alpha_(1)T)+R_(0)(1+alpha_(2)T)`
where, `R_(s0)=R_(0)+R_(0)=2R_(0)`
`therefore 2R_(0)(1+alpha_(s)T)=2R_(0)+R_(0)T(alpha_(1)+alpha_(2))`
`2R_(0)+2R_(0)alpha_(s)T=2R_(0)+R_(0)T(alpha_(1)+alpha_(2))therefore alpha_(s)=(alpha_(1)+alpha_(2))/(2)`