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

Answer

b

Explanation

Effective resistance of two wires in series is
`R_(eff) = R_(1) + R_(2) = (l)/(sigma_(1)A) + (l)/(sigma_(2)A)`
`R_(eff) = (2l)/(sigma_(eq)A)`
`(2l)/(sigma_(eq)A) = (l)/(A)[(1)/(sigma_(1)) + (1)/(sigma_(2))] = (l(sigma + sigma_(2)))/(A sigma_(1)sigma_(2))`
`sigma_(eff) = (2sigma_(1)sigma_(2))/(sigma_(1) + sigma_(2))`