Question

A potentiometer has a uniform potential gradient across it. Two cells connected in series - (i) to support each other and (ii) to oppose each other are balanced over 6 m and 2 m respectively on the potentiometer wire. The emfs of the cells are in the ratio

• A. 1 : 4
• B. 1 : 1
• C. 3 : 1
• D. 2 : 1

Answer 1

The correct option is D 2 : 1

Let, the $L$ lenght wire having resistance of $R_0$,
then, the resistance of $x$ wire =$\frac{x{R}_0}{L}$

Case-1: In support condition

$E_1+E_2=\frac{6R_0}{L}$ ....(1)

Case 2: In oppose condition

$E_1-E_2=\frac{2R_0}{L}$ ....(2)

$\frac{Eq.\left(1\right)}{Eq.\left(2\right)}=\frac{E_1+E_2}{E_1-E_2}=\frac{3}{1}{E}_1+E_2=3(E_1-E_2)$

Hence, $\frac{E_1}{E_2}=\frac{2}{1}$
$E_1:E_2=2:1$

hence, option (d) is correct.