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www.GOALias.blogspot.com122PhysicsFIGURE 3.28 A potentiometer. G isa galvanometer and R a variableresistance (rheostat). 1, 2, 3 areterminals of a two way key(a) circuit for comparing emfs of twocells; (b) circuit for determininginternal resistance of a cell.3.16 POTENTIOMETERThis is a versatile instrument. It is basically a long piece of uniform wire,sometimes a few meters in length across which a standard cell isconnected. In actual design, the wire is sometimes cut in several piecesplaced side by side and connected at the ends by thick metal strip.(Fig. 3.28). In the figure, the wires run from A to C. The small verticalportions are the thick metal strips connecting the various sections ofthe wire.A current I flows through the wire which can be varied by a variableresistance (rheostat, R) in the circuit. Since the wire is uniform, thepotential difference between A and any point at a distance l from A isε()l = φl (3.89)where φ is the potential drop per unit length.Figure 3.28 (a) shows an application of the potentiometer to comparethe emf of two cells of emf ε 1and ε 2. The points marked 1, 2, 3 form a twoway key. Consider first a position of the key where 1 and 3 are connectedso that the galvanometer is connected to ε 1. The jockeyis moved along the wire till at a point N 1, at a distance l 1from A, there is no deflection in the galvanometer. Wecan apply Kirchhoff’s loop rule to the closed loopAN 1G31A and get,φ l 1+ 0 – ε 1= 0 (3.90)Similarly, if another emf ε 2is balanced against l 2(AN 2)φ l 2+ 0 – ε 2= 0 (3.91)From the last two equationsε1 l1ε = 2l(3.92)2This simple mechanism thus allows one to comparethe emf’s of any two sources. In practice one of the cellsis chosen as a standard cell whose emf is known to ahigh degree of accuracy. The emf of the other cell is theneasily calculated from Eq. (3.92).We can also use a potentiometer to measure internalresistance of a cell [Fig. 3.28 (b)]. For this the cell (emf ε )whose internal resistance (r) is to be determined isconnected across a resistance box through a key K 2, asshown in the figure. With key K 2open, balance isobtained at length l 1(AN 1). Then,ε = φ l 1[3.93(a)]When key K 2is closed, the cell sends a current (I )through the resistance box (R). If V is the terminalpotential difference of the cell and balance is obtained atlength l 2(AN 2),V = φ l 2[3.93(b)]