Question

Consider the potentiometer circuit as arranged in the figure (32−E29). The potentiometer wire is 600 cm long. (a) At what distance from the point A should the jockey touch the wire to get zero deflection in the galvanometer? (b) If the jockey touches the wire at a distance of 560 cm from A, what will be the current in the galvanometer?
Figure

Answer 1

Explanation:

On the wire, let the null point be X at a distance x cm from point A, as shown.

Given:

Of the wire AB, the total resistance = 15r

Per unit cm, the resistance = 15r600

Resistance of x cm of the wire = 15r x 600

The wire’s resistance of (600 – x) cm of the wire =

15r600-$\times$600  

(a) In loop 1, applying KVL, we obtain:

i1 + 15600r600 + i215600rx + i1r - xi1 = ε        …i

In loop 2, applying KVL, we obtain:

i2r + 15600rx i1 + i2 = ε2    …(ii)

In the galvanometer, for zero deflection, i2 = 0.  

From equation (ii),

15600r x i1 = ε2 ⇒ i1 = 20εrx

When the values of i1 and i2 are substituted in equation (i), we obtain:

x = 320 cm

(b) Solving equations (i) and (ii) by putting x = 560 cm, we obtain:

i2 = 3ε22r