Combination of Batteries: Practice Problem & Solution

Solution Explained:

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

Total current $I = \frac{2E}{R + r_1 + r_2}$. The potential difference across the first cell is $V_1 = E - Ir_1 = 0$, meaning $E = Ir_1$. Substituting $I$, we get $E = \frac{2E r_1}{R + r_1 + r_2}$. Simplifying gives $R + r_1 + r_2 = 2r_1$, so $R = r_1 - r_2$.