Potentiometer

The potentiometer is an instrument built for very accurate, null-method measurement of potential differences, currents and resistances -- more accurate, in fact, than a direct voltmeter reading, precisely because at the balance point it draws no current at all from the circuit being measured. It consists of a very long uniform wire (of manganin or constantan), typically stretched as ten separate one-metre-long rows on a wooden board, with the free ends A and B of the whole run brought together to the same side and fixed to copper terminal strips; a metre scale, fixed alongside the wire, and a sliding jockey complete the apparatus.

The battery Bt, a key K, and the potentiometer wire (from C to D) are connected in series, forming the primary circuit, which drives a steady current through the whole wire (Figure 2.27). The secondary circuit connects the positive terminal of a test cell of emf $\varepsilon$ to point C, with its negative terminal connected through a galvanometer G and a high resistance HR to a sliding jockey. If the jockey makes contact at some point J on the wire, and the potential difference across the length CJ happens to exactly equal the cell's emf $\varepsilon$, no current at all flows through the galvanometer, which shows zero deflection -- this null point defines the balancing length, $l = CJ$. The potential difference across CJ is $Irl$, where I is the (steady) current in the primary circuit and r is the wire's resistance per unit length, so at balance,

$\varepsilon = I\,r\,l \qquad (2.58)$ …