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?

Answer 1

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:
$\left(i_1+i_2\right)\frac{15}{600}rx+\frac{15}{600}r\left(600-x\right)i_1+i_{1}r=\epsilon ...\left(\mathrm{i}\right)$

Applying KVL in loop 2, we get:
$i_{2}r+\frac{15}{600}rx\left(i_1+i_2\right)=\frac{\epsilon }{2}...\left(\mathrm{ii}\right)$
For zero deflection in the galvanometer, i₂ = 0. From equation (ii),
$$\begin{gathered} \frac{15}{600}rx\left(i_1\right)=\frac{\epsilon }{2} \\ \Rightarrow i_1=\frac{20\epsilon }{rx} \end{gathered}$$
Substituting the values of i₁ and i₂ in equation (i), we get:
x = 320 cm

(b) Putting x = 560 cm and solving equations (i) and (ii), we get:
$i_2=\frac{3\epsilon }{22r}$