A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. E0 and a resistance r1. An unknown e.m.f. E is balanced at a length l of the potentiometer wire. The e.m.f. E will be given by :
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Explanation:

The current through the potentiometer wire is

and the potential difference across the wire is

The potential gradient along the potentiometer wire is

As the unknown e.m.f. E is balanced against length l of the potentiometer wire,

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