Question

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

• A. $2\Omega$
• B. $4\Omega$
• C. $6\Omega$
• D. $8\Omega$

Answer 1

The correct option is B $4\Omega$

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