Figure shows a long potentiometer wire AB having a constant potential gradient. The null points for the two primary cells of emfs `epsi _(1) and epsi _(2)` connected in the manner shown are obtained at a distance of `l _(1) = 120 cm and l _(2) = 300 cm ` from the end A. Determine `(i) epsi _(1) //epsi _(2)` and (ii) position of null point for the cell `epsi _(1)` only.

Explanation

(i) `(epsi _(1) - epsi _(2))/( epsi _(1) + epsi _(2)) = (120)/( 300 ) = 2/5`
`(epsi _(1))/( epsi _(2)) = 7/3`
(ii) `(epsi _(1) + epsi _(2))/( epsi _(1)) = (300 )/(x ) implies ( 300 )/( x ) = (10)/(7)`
`implies x = 210 cm`
(where x is the position of null point with cell `epsi _(1)`).