Two metal wires of identical dimesnios are connected in series. If `sigma_(1)` and `sigma_(2)` are the conducties of the metal wires respectively, the effective conductivity of the combination is

Options

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

Answer

B

Explanation

`R_(eq)=R_(1)+R_(2)`
`rArr (2l)/(sigma_(eq)A)=(l)/(sigma_(1)A)+(l)/(sigma_(2)A) rArr sigma_(eq)=(2sigma_(1)sigma_(2))/(sigma_(1)+sigma_(2))`