Combination of Resistors: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:

In series combination, $R_{eq} = R_1 + R_2$. Using $R = \frac{l}{\sigma A}$, we get $\frac{2l}{\sigma_{eq} A} = \frac{l}{\sigma_1 A} + \frac{l}{\sigma_2 A}$. Therefore, $\frac{2}{\sigma_{eq}} = \frac{1}{\sigma_1} + \frac{1}{\sigma_2}$, which gives $\sigma_{eq} = \frac{2\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$.