Question

One of the circuits for the measurement of resistance using potentiometer is as shown. The galvanometer is connected at point $A$ and zero deflection is observed at length $PJ=30\text{cm}.$ In second case the secondary cell is changed and the zero deflection is observed at length $PJ=10\text{cm}.$The resistance $R$ (in ohm) is?
For $1^{st}\text{case},$ take ${ϵ}_s=10\text{V}$ and $r=1\Omega$ and for $2^{nd}\text{case},$ take ${ϵ}_s=5\text{V}$ and $r=2\Omega$

Answer 1

Assume that potential gradient is $G$
For null point at $l$ from P, $Gl=\frac{ϵR}{R+r}$

For $1^{st}$ case

$G\times 30$ = $\frac{10}{R+1}\times R$ $...\left(1\right)$
$2^{nd}$ case
$G\times 10$ = $\frac{5}{R+2}\times R$ $...\left(2\right)$
on dividing equations,
$\frac{30}{10}$ = $\frac{10R}{R+1}\times \frac{R+2}{5R}$
$\Rightarrow 3=\frac{2(R+2)}{R+1}$
$\Rightarrow 3R+3=2R+4$
$\Rightarrow R=1\Omega$
Ans : $1.00$