A potentiometer can measure emf of a cell because

The potentiometer is preferred over voltmeter for measurement of emf of cell because the potentiometer does not draw any current for itself from the primary circuit. Therefore it gives more accurate measurement thereby acting as an ideal voltmeter.

A voltmeter draws current from a cell, therefore voltmeter measure terminal potential difference rather than emf, while a potentiometer at balance, does not draw any current from the cell; so the cell remains in open circuit. Hence potentiometer reasds the actual value of emf.

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