Question

Consider the potentimeter circuit arranged as in figure. The potentometer wire is $600cm$ 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 $560cm$ from A, what will be the current in the galvanometer?

Answer 1

(i) $\frac{E}{2}=(15-x)r{I}_1$

$\Rightarrow E=2(15-x)r{I}_1....\left(i\right)$

and

$E=(15-x)r{I}_1+(1+x)r{I}_1$

$=16r{I}_1......\left(ii\right)$

Eq $\left(i\right)=\left(ii\right)$

$2(15-x)=16\Rightarrow 30-2x=165\Rightarrow x=7$

Let Jockey be places your from left

$\therefore \frac{y}{600-y}=\frac{15-x}{x}=\frac{8}{7}$

$\Rightarrow 7y=4800-8y\Rightarrow y=\frac{4800}{15}=320cm$

(ii) Since $600cm=15r$, therefore

$560cm=14r$

$\frac{E}{2}=14r(I_1+I_2)+I_{2}r$

$\Rightarrow E=r(28I_1+30I_2)$

$\Rightarrow E=14r(I_1+I_2)+2r\left(I_1\right)$

$=r(16I_1+14I_2)$

By solving above equation

$I_2=\frac{3E}{22r}$