. P OTENTIOMETER This is a versatile instrument. It is basically a long piece of uniform wire, sometimes a few meters in length across which a standard cell is connected. In actual design, the wire is sometimes cut in several pieces placed side by side and connected at the ends by thick metal strip.
(Fig. . ). In the figure, the wires run from A to C.
The small vertical portions are the thick metal strips connecting the various sections of the wire. A current I flows through the wire which can be varied by a variable resistance (rheostat, R ) in the circuit. Since the wire is uniform, the potential difference between A and any point at a distance l from A is ( ) φ l l ( . ) where φ is the potential drop per unit length.
Figure . (a) shows an application of the potentiometer to compare the emf of two cells of emf ε and ε . The points marked , , form a two way key. Consider first a position of the key where and are connected so that the galvanometer is connected to ε .
The jockey is moved along the wire till at a point N , at a distance l from A, there is no deflection in the galvanometer. We can apply Kirchhoff’s loop rule to the closed loop AN G31A and get, φ l + – ε = ( . ) Similarly, if another emf ε is balanced against l (AN ) φ l + – ε = ( . ) From the last two equations l l ε = ( .
) This simple mechanism thus allows one to compare the emf’s of any two sources. In practice one of the cells is chosen as a standard cell whose emf is known to a high degree of accuracy. The emf of the other cell is then easily calculated from Eq. ( .
). We can also use a potentiometer to measure internal resistance of a cell [Fig. . (b)].
For this the cell (emf ε ) whose internal resistance ( r ) is to be determined is connected across a resistance box through a key K , as shown in the figure. With key K open, balance is obtained at length l (AN ). Then, ε = φ l [ . (a)] When key K is closed, the cell sends a current ( I ) through the resistance box ( R ).
If V is the terminal potential difference of the cell and balance is obtained at length l (AN ), V = φ l [ . (b)] FIGURE . A potentiometer. G is a galvanometer and R a variable resistance (rheostat).
, , are terminals of a two way key (a) circuit for comparing emfs of two cells; (b) circuit for determining internal resistance of a cell.