Question

A potentiometer wire $AB$ is $100cm$ long and has a total resistance of $10ohm$. If the galvanometer shows zero deflection at the position $C$, then find the value of unknown resistance $R$. (in $\Omega$ )

Answer 1

Answer: 4.00

Potential gradient
$x=$ current $\times$ Resistance per unit length
$x=\frac{10V}{10\Omega }\times \frac{10}{100}$
$x=0.1V/cm$
Potential difference across $R$ is balanced at $40cm$.
$\therefore V=x\times 40$
$V=0.1\times 40=4$ volt.
But $V=I\times R$
$4=\left(\frac{5}{R+1}\right)R$
$\Rightarrow 4R+4=5R$
$\Rightarrow R=4\Omega$