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. `(2 sigma_(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

(b) `R_(eq) = R_(1) + R_(2)` ltbgt `implies (2l)/(sigma_(eq) A) = (l)/(sigma_(1) A) + (l)/(sigma_(2) A) implies sigma_(eq) = (2 sigma_(1) sigma_(2))/(sigma_(1) + sigma_(2))`