A potentiometer wire of length and resistance L and R respectively are connected in series with emf E0 and resistance R1. One unknown emf E is balanced at length of potentiometer wire. Find emf.

The schematic diagram of the given question is can be illustrated as:

EMF

Current that passes via the potentiometer wire is:

= \(I = \frac{E_0}{r\ +\ r_1}\)

The potential differ nce in the wire equals:

= \(V = Ir = \frac{E_0r}{r\ +\ r_1}\)

Along the potentiometer, the potential gradient is:

\(\therefore\) \(kl = \frac{E_0r}{r\ +\ r_1L}\)

Thus, the unknown emf equals: \(\frac{E_0r}{r\ +\ r_1L}\)

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