A resistance R is connected across a cell of emf `epsilon` and internal resistance r. A potentiometer now measures the potential difference between the terminals of the cell is V. Write the expression for r in terms of `epsilon`, V and R`.

Explanation

To find the expression for the internal resistance \( r \) in terms of the EMF \( \epsilon \), the potential difference \( V \), and the external resistance \( R \), we can follow these steps:

### Step 1: Understand the circuit
We have a cell with an EMF \( \epsilon \) and internal resistance \( r \) connected to an external resistance \( R \). When a current \( I \) flows through the circuit, there will be a potential drop across both the internal and external resistances.

### Step 2: Write the equations for the circuit
According to Ohm's law, the total EMF in the circuit can be expressed as:
\[
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