There is a definite potential difference between the two ends of a potentiometer. Two cells are connected in such a way that first time help each other, and second time they oppose each other. They are balanced on the potentiometer wire at 120cm and 60cm length respectively. compare the electromotive force of the cells. potentiometer wire at 120cm and 60cm length respectively. Compare the electromotive force of the cells.

Explanation

Suppose the potential gradient along the potentiometer wire=x
and the emf's of the two cells are `E_(1)` and `E_(2)`.
When the cells help each other, the resultant emf=`(E_(1)+E_(2))`
`E_(1)+E_(2)=x xx 120cm`.
When the cells oppose each other, the resultant emf`=(E_(1)-E_(2))`
`E_(1)-E_(2)=x xx60cm`.
From equation (i) and (ii)
`(E_(1)+E_(2))/(E_(1)-E_(2))=(120cm)/( 6 0cm)=(2)/(1)` or `E_(1)+E_(2)=2(E_(1)-E_(2))` or `3E_(2)=E_(1)` or `(E_(1))/(E_(2))=(3)/(1)`