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 cmfrom the end A. Determine (i) epsi _(1) //epsi _(2) and (ii) position of null point for the cell epsi _(1) only.

Figure shows a long potentiometer wire AB having a constant potential

1.	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 cmfrom the end A. Determine (i) epsi _(1) //epsi _(2) and (ii) position of null point for the cell epsi _(1) only.
Answer» Solution :(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)`).

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