1.

Two metal wires of identical dimensions are connected in series. If sigma_(1) and sigma_(2)are the conductivities of the metal wires respectively, the effective conductivity of the combination is

Answer»

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

SOLUTION :`(2 sigma_(1) sigma_(2))/(sigma_(1) + sigma_(2))`
Effective resistor R `R_(1) + R_(2) `....(1)
But `R_(1) = (l)/(sigma_(1)A) and R_(2) = (l)/(sigma_(2)A)`
`[ therefore R = (RHO l)/(A) and sigma = (1)/(gamma) ]`
From EQ. (1) `(2l)/(sigma A) = (l)/(sigma_(1)A) + (l)/(sigma_(2)A) [ therefore R = (2l)/(sigma A)] `
`(2)/(sigma)= (1)/(sigma_(1)) + (1)/(sigma_(2)) = (sigma_(1) + sigma_(2))/(sigma_(1) sigma_(2))` ,
`therefore sigma = (2 sigma_(1) sigma_(2))/(sigma_(1) + sigma_(2))`


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