A resistance R is connected across a cell of emf E and internal resistance r. Why does potentiometer now measure the potential difference between the terminals of the cell,as V?
The potential difference between the electrodes of a cell is equal to E when no current is flowing through the cell.
When a resistor R is connected across the cell, current I flows through the cell.
If the cell has internal resistance, then the potential difference will become E - Ir.
Therefore, the potentiometer measures V and not E.