# To compare the e.m.f.s of two cells by using a potentiometer

To compare the e.m.f.s of two cells by using a potentiometer

In the circuit diagram of Fig. 40.7 the points D and F may be considered as the two terminals of a voltmeter. D is connected directly to ·A, and F is connected to a sliding contact on the potentiometer wire via a sensitive centre-zero galvanometer. As it is
easy to damage the galvanometer by too large a current if contact is made on the wire too far from the balance point, a safety resistor of 1000 n or more is placed in series with the galvanometer to protect it by limiting the current. Once the balance
point has been located approximately, the safety resistor is shorted out by closing the key K, and the final adjustment made with the galvanometer at maximum sensitivity.

With the circuit as shown in Fig. 40.7 there will be a potential difference between D and F equal to that between A and C on the poten-tiometer wire. This potential difference can be varied by altering the position of C, and will be proportional to the length A C. In the diagram D will be positive relative to F, since the positive terminal of the cell E is connected to A.

Suppose we wish to compare the e.rn.f.s of two cells. The two points D and Fare connected to the terminals of the first cell E1 (Fig. 40.7) just as the leads from a voltmeter would be connected across the cell, care being taken to connect D to the positive terminal of the cell. On making contact with the jockey on the wire at C current will, in general, flow through the galvanometer in one direction or the other, depending on whether the e.m.f. of E1 is greater or less than the potential difference between D and F. The position of C is now adjusted until no current is indicated by the galvanometer. This will occur when the potential difference between D and F (and therefore between A and C) is equal to the e.m.f. of the cell E1• Note that the p.d. across the terminals of E1 is equal to its e.m.f. because the cell is delivering no current. We now note the length AC, say /1′

The experiment is repeated using the second cell E2 and the corresponding length /2 obtained. Since the wire is uniform, the p.d. between any two points on the wire will be directly proportional to the length of wire between them. ‘Therefore, since /1 and /2 are the lengths corresponding to the e.m.f.s of E1 and E2 respectively.

When the experiment is carried out as described above the result is simply the ratio of the e.mJ. of the two cells concerned. However, a special cell called a Weston cadmium standard cell, which has an e.rn.f of 1.02 V, can be used to standardize a potentiometer so that it can be used to measure e.m.f. Thus if the balance length for a Weston cell is /2 in em, then in volts.