WBJEE · Physics · Current Electricity
Two metal wires of identical dimensions are connected in series. If \(\sigma_{1}\) and \(\sigma_{2}\) are the electrical conductivities of the metal wires respectively, the effective conductivity of the combination is
- A \(\sigma_{1}+\sigma_{2}\)
- B \(\frac{\sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}\)
- C \(\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}\)
- D \(\frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}}\)
Answer & Solution
Correct Answer
(C) \(\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}\)
Step-by-step Solution
Detailed explanation
\(R_{e q}=R_{1}+R_{2}\) \(\frac{1}{\sigma_{e q}} \frac{2 l}{A}=\frac{1}{\sigma_{1}} \frac{1}{A}+\frac{1}{\sigma_{2}} \frac{1}{A}\left[\sigma_{e q}=\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}\right]\)
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