A

To determine the current through resistance R connected in series with two cells, we can use Kirchhoff's laws.
1. **Total EMF**: The total EMF in the circuit is the sum of the EMFs from both cells, which is 2e.
2. **Total Internal Resistance**: The total internal resistance is r1 + r2.
3. **Total Resistance in Circuit**: The total resistance of the circuit is R (external resistance) + r1 + r2.
4. **Current Calculation**: Using Ohm’s law, the total current (I) flowing in the circuit can be given by the formula:
$$ I = \frac{\text{Total EMF}}{\text{Total Resistance}} = \frac{2e}{R + r_1 + r_2} $$
5. **Potential Drop Across Each Cell**: To find the potential drop across the second cell, we can use the formula:
$$ V_{r_2} = I \cdot r_2 $$
If the external resistance R is equal to r2 - r1, the potential drop across the second cell becomes zero when there is no current flow.
Therefore, option A is correct.