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 ohms

Answer 1

Given : $E=10$ volts $L=AB=100$ cm

Thus potential difference A and C $V_{AC}=\frac{E}{AB}\times AC=\frac{10}{100}\times 40=4$ volts

$\therefore$ $V_{BG}=V_{PM}=V_{AC}=4$ volts

Using $V_{BG}=5-Ir$ where $r=1\Omega$

$\therefore$ $4=5-I\left(1\right)$ $⟹I=1$ A

Thus resistance $R=\frac{V_{PM}}{I}=\frac{4}{1}=4\Omega$