Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are` R_(1) and R_(2) (R_(1) gt R_(1))`. If the potential difference across the source having internal resistance `R_(2)` is zero, then

Options

A. `R=((R_2 times (R_1+R_2))/((R_2-R_1)`
B. `R=R_2-R_1`
C. `R=(R_1R_2)/((R_1+R_2)`
D. `R=(R_1R_2)/((R_2-R_1))`

Explanation

To solve the problem, we need to analyze the circuit with two sources of equal emf connected to an external resistance \( R \) and internal resistances \( R_1 \) and \( R_2 \). We know that the potential difference across the source with internal resistance \( R_2 \) is zero. Let's break down the solution step by step.

### Step 1: Understand the Circuit
We have two sources of equal emf \( E \) connected in parallel to an external resistance \( R \). The internal resistances of the sources are \( R_1 \) and \( R_2 \).

### Step 2: Write the Expression for Current
The total current \( I \) flowing through the circuit can be expressed as:
\[
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