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

Answer

D

Explanation

`therefore rho = (rho_(1) + rho_(2))/2`
`rArr 1/sigma =(1/sigma_(1) + 1/sigma_(2))/2 = (sigma_(1) + sigma_(2))/(2 sigma_(1) sigma_(2)) rArr sigma =(2 sigma_(1) sigma_(2))/(sigma_(1) + sigma_(2))`