Potentiometer — EMF Comparison

Two EMFs are compared by finding their balance lengths l₁ and l₂ on the potentiometer wire. At balance, no current is drawn from the cell — gives true EMF, not terminal voltage.

Principle

A driver cell maintains a steady current $I$ through a long uniform wire of resistance $r$ per unit length. Potential drop per unit length: $\phi = Ir$ (a constant).

Potential at length $l$ from the start: $V(l) = \phi l$

Balance condition

A cell of EMF $\mathcal{E}$ is connected with its positive terminal to the high-potential end of the wire. The jockey is moved until the galvanometer reads zero — no current flows from the test cell at length $l$.

At balance: $\mathcal{E} = \phi l$

Since no current flows from the test cell, there is no drop across its internal resistance. The potentiometer measures true EMF, not terminal voltage.

Comparing two EMFs

$$\mathcal{E}_1 = \phi l_1, \quad \mathcal{E}_2 = \phi l_2$$ $$\boxed{\frac{\mathcal{E}_1}{\mathcal{E}_2} = \frac{l_1}{l_2}}$$

Advantage over voltmeter

A voltmeter draws current, causing a terminal voltage drop. The potentiometer at balance draws zero current — gives the true EMF directly.