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Two metal wires of identical dimesnios a...

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

A

`(sigma_1 + sigma_2)/(2 sigma_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)`

Text Solution

Verified by Experts

The correct Answer is:
D
In figure, two metal wires of identical dimension are connected in series

`R_("eq") = ( l)/( sigma_(1) A) + (1)/( sigma_(2) A) = (l_("eq"))/( sigma_("eq") A_("eq")) " "therefore sigma_("eq") = (2 sigma_(1) sigma_(2))/( sigma_(1) + sigma_(2))`
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