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Question: If σ<sub>1</sub>, σ<sub>2</sub> and σ<sub>3</sub> are the conductances of three conductors, then the...

If σ1, σ2 and σ3 are the conductances of three conductors, then their equivalent conductance, when they are joined in series will be –

A

σ1 + σ2 + σ3

B

1σ1\frac{1}{\sigma_{1}} + 1σ2\frac{1}{\sigma_{2}} + 1σ3\frac{1}{\sigma_{3}}

C

σ1σ2σ3σ1+σ2+σ3\frac{\sigma_{1}\sigma_{2}\sigma_{3}}{\sigma_{1} + \sigma_{2} + \sigma_{3}}

D

None of these

Answer

None of these

Explanation

Solution

R = R1 + R2 + R3

1σ\frac{1}{\sigma} = 1σ1\frac{1}{\sigma_{1}} + 1σ2\frac{1}{\sigma_{2}} + 1σ3\frac{1}{\sigma_{3}}

⇒ σ = (1σ1+1σ2+1σ3)–1\left( \frac{1}{\sigma_{1}} + \frac{1}{\sigma_{2}} + \frac{1}{\sigma_{3}} \right)^{–1}