A cell of emf E is connected across an external resistance R. When a current 'I' is drawn from the cell, the potential difference across the electrodes of the cell drops to 'V'. The internal resistance 'r' of the cell is

$\left[\frac{E-V}{V}\right]R$

The correct answer is Option (4) → $\left[\frac{E-V}{V}\right]R$

Ohm's law for a cell with internal resistance $r$:

$V = E - I r$

Solving for $r$:

$r = \frac{E - V}{I}=\left[\frac{E-V}{V}\right]R$

Final Answer: $r = \left[\frac{E-V}{V}\right]R$