The Potentiometer

• A driver cell pushes a steady current through a uniform resistance wire XY.
• Uniform means every centimetre of wire has the same resistance. So the piece of wire from X to any point is a resistor, and its resistance grows in proportion to its length.
• That makes the wire a potential divider with a sliding contact: the piece from X takes a share of the wire's p.d. equal to its share of the length.
• Small numbers: a 100 cm wire with 2.0 V across it has 0.020 V on every centimetre. From X to the 25 cm mark the p.d. is 0.50 V; to the 75 cm mark it is 1.5 V.
• So the position of the contact gives you any p.d. from 0 up to the whole wire's p.d. You choose the p.d. by choosing the length.

• The test cell E connects X to a sliding contact, the jockey, through a galvanometer: a sensitive current detector that is only used here to show zero.
• That small loop now holds two voltages facing each other: the test cell's e.m.f. E, and the wire's p.d. between X and the jockey.
• If the wire's p.d. is bigger than E, it drives a current through the galvanometer one way. If it is smaller than E, the test cell drives a current the other way.
• Slide the jockey until the galvanometer reads exactly zero. At that position the two p.d.s are equal: nothing is left to drive a current round the small loop. This position is the balance point, and the whole approach is a null method.

• At balance the test cell delivers no current. No current means no lost volts: $Ir = 0$, whatever r is.
• So the wire's p.d. is matched to the cell's true e.m.f., not its terminal p.d.
• A voltmeter can never do this: it always takes some current to work.

The potentiometer reads the true e.m.f. because at balance it takes no current. Use that sentence whenever the exam asks why a potentiometer is better than a voltmeter.