Current Electricity

In a potentiometer experiment, we measure the emf (E) of the cell (open circuit) and the terminal voltage (V) when a known external resistance (R) is connected (closed circuit). The emf corresponds to a balancing length , and the terminal voltage corresponds to a balancing length . So, and .
The relationship between emf, terminal voltage, and internal resistance (r) is and .
Dividing the two equations gives .
Rearranging for r: , which gives . Since , this is also written as .

A potentiometer has several advantages over a voltmeter for measuring potential difference:
Greater Accuracy: A potentiometer is more accurate because it works on the null deflection method. At the balance point, it draws no current from the circuit whose potential difference is being measured. In contrast, a voltmeter always draws some current, which alters the potential difference it is intended to measure.
Measures EMF Accurately: Because it draws no current at balance, a potentiometer can measure the true electromotive force (e.m.f.) of a cell. A voltmeter measures the terminal potential difference, which is less than the e.m.f. when current is flowing.
High Sensitivity: The sensitivity of a potentiometer is very high and can be easily increased by increasing the length of the potentiometer wire.
Versatility: A potentiometer is a versatile instrument that can also be used to compare the e.m.f.s of two cells and to determine the internal resistance of a cell.