Question

The two cells are connected in series, in a potentiometer experiment, in such a way so as to support each other and to oppose each other. The balancing lengths in two conditions are obtained as 150 cm and 50 cm respectively. The ratio of emf's of two cells will be

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is B 2:1

Let, $E_1$ and $E_2$ be the emf's of two cells, $l_1$ and $l_2$ be

the balancing lengths obtained for two cells respectively.

When the cells support each other,

$E_1+E_2=l_1+l_2$..........................$(\because E\propto l)$

When the cells oppose each other,

$E_1-E_2=l_1-l_2$

But, $l_1+l_2=150cm$...............................$\left(1\right)$

and $l_1-l_2=50cm$....................................$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we get,

$2l_1=200cm$

$l_1=100cm$

Using this in $\left(1\right)$, we get,

$l_2=50cm$
Thereore,

$\frac{l_1}{l_2}=\frac{100}{50}=\frac{2}{1}$