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)`
`rho(2L)/(A)=rho_(1)(L)/(A)+rho_(2)(L)/(A)`
`2rho=rho_(1)+rho_(2)`
`(2)/(sigma)=(1)/(sigma_(1))+(1)/(sigma_(2))`
`(2)/(sigma)=(sigma_(1)+sigma_(2))/(sigma_(1)sigma_(2))`
`sigma=(2sigma_(1)sigma_(2))/(sigma_(1)+sigma_(2))`