Two cells of same emf E, but different internal resistances `r_(1)andr_(2)` are connected to an external
resistance R as shown in the figure given above. The voltmeter V reads zero. Obtain an expression for R in terms of `r_(1)andr_(2)`. Calculate the voltage across the cell of internal resistance `r_(2)`. (Assume that the voltmeter V is of infinite resistance).

Explanation

To solve the problem, we need to analyze the circuit with two cells of the same emf \( E \) but different internal resistances \( r_1 \) and \( r_2 \) connected to an external resistance \( R \). The voltmeter \( V \) reads zero, which indicates that there is no potential difference across it.

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- We have two cells in series, each with an emf \( E \) and internal resistances \( r_1 \) and \( r_2 \).
- The total emf in the circuit is \( 2E \) (since both cells contribute).
- The total internal resistance is \( r_1 + r_2 \).
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