Consider the potentiometer circuit as arranged in the figure. 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?

#### Solution

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

Given:-

Total resistance of the wire AB = 15r

Resistance per unit cm = \[\frac{15r}{600}\]

Resistance of x cm of the wire = \[\frac{15rx}{600}\]

Resistance of (600 - x ) cm of the wire = \[\frac{15r\left( 600 - x \right)}{600}\]

(a) Applying KVL in loop 1, we get:-

\[\left( i_1 + i_2 \right)\frac{15}{600}rx + \frac{15}{600}r\left( 600 - x \right) i_1 + i_1 r = \epsilon...........(1)\]

Applying KVL in loop 2, we get:-

\[i_2 r + \frac{15}{600}rx \left( i_1 + i_2 \right) = \frac{\epsilon}{2}............(2)\]

For zero deflection in the galvanometer, i_{2} = 0. From equation (2),

\[\frac{15}{600}rx\left( i_1 \right) = \frac{\epsilon}{2}\]

\[ \Rightarrow i_1 = \frac{20\epsilon}{rx}\]

Substituting the values of i_{1} and i_{2} in equation (1), we get:-

x = 320 cm

(b) Putting x = 560 cm and solving equations (1) and (2), we get:-

\[i_2 = \frac{3\epsilon}{22r}\]