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

Question

A 2 Ω resistor is connected in series with R Ω resistor. This coinbination is connected across a cell. When the potential difference across 2 Ω resistor is balanced on potentiometer wire, null point is obtained at a length of 300 cm. When the same procedure is repeated for R Ω resistor, null point is obtained at the length of 350 cm, value of R is : (A) 5 Ω  (B) 3.33 Ω  (C) 4.6 Ω  (D) 2.33 Ω

Tardigrade Admin · Accepted Answer

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

∴ \frac{R}{2} = \frac{350}{300}

\Rightarrow R = 2.33 Ω

$5 Ω$

$3.33 Ω$

$4.6 Ω$

$2.33 Ω$

5Ω

3.33Ω

4.6Ω

2.33Ω

$5 Ω$

$3.33 Ω$

$4.6 Ω$

$2.33 Ω$