Question

A $2 \Omega$ resistor is connected in series with $R \Omega$ resistor. This coinbination is connected across a cell. When the potential difference across $2 \Omega$ resistor is balanced on potentiometer wire, null point is obtained at a length of $300\, cm$. When the same procedure is repeated for $R \Omega$ resistor, null point is obtained at the length of $350 cm$, value of $R$ is :

• A. $5 \, \Omega $
• B. $3.33 \, \Omega $
• C. $4.6 \, \Omega $
• D. $2.33 \, \Omega $

Answer 1

Answer: (D)

It is evident from the diagram that between $J_{1}$ and $J_{2}$ there will be a point $J$ such that when the jockey is made to touch $J$, there will be no deflection in the galvanometer.
As per principle of potentiometer when a constant current is passed through a wire of uniform cross-section the potential difference across any portion of wire is directly
proportional to the length.

$E=K l$
First case,
$\frac{E}{2+R} \times 2=300 \,K$
Second case,
$\frac{E}{2+R} \times R =350 \,K $
$\therefore \frac{R}{2} =\frac{350}{300}$
$\Rightarrow R =2.33 \,\Omega$