Question

Two metal wires of same length, same area of cross-section have conductivities of their material \( \sigma_1 \) and \( \sigma_2 \). If they are connected in series, the effective conductivity is:

• A. \( \frac{\sigma_1 \sigma_2}{\sigma_1 + \sigma_2} \)
• B. \( \frac{2 \sigma_1 \sigma_2}{\sigma_1 + \sigma_2} \)
• C. \( \frac{\sigma_1}{\sigma_2} \)
• D. \( \frac{2 \sigma_1}{\sigma_2} \)

Hint:

For conductors in series, use the formula \( \frac{2 \sigma_1 \sigma_2}{\sigma_1 + \sigma_2} \) to find the effective conductivity.

Answer 1

The Correct Option is B

When two conductors are connected in series, the effective conductivity is given by \( \frac{2 \sigma_1 \sigma_2}{\sigma_1 + \sigma_2} \), which is similar to the formula for resistances in parallel. Thus, the correct answer is option (2).