Two cells of same emf `epsi` but internal resistances `r_1` and `r_2` are connected in series to an external resistor R. What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

Explanation

Here net emf of combination = `2epsi` and net resistance of the circuit = `r_1 + r_2 + R`
Current flowing in the circuit `I = (2 epsi)/(r_1 + r_2 + R)`
As potential difference across first cell `V_1 = epsi - Ir_1 = 0, ` hence
`epsi - (2epsi)/((r_1 + r_2 + R)) r_1 = 0 ` or `epsi[r_1 + r_2 + R - 2r_1] = 0`
` rArr R = r_1 - R_2 `