The length of a potentiometer wires is l. A cell of emf (E ) is balanced at a length ( ( l 3 ) ) from positive end of the wire. If the length of the wire is increased by ( ( l 2 ) ), the distance at which the same cell gives the balancing point is (Cell in the primary is ideal and no series resistance is present in the primary circuit.)

Step-by-step solution

According to question, the figure is as If (K ) be the potential gradient of the potentiometer wire, then emf of the cell which gives balancing length ( l 3 ) is given by (E=K l 3 )...(i) Where, ( E= V l l 3 = V 3 ) (ii) ( [ K= V l ] ) When, length of potentiometer wire is increased by ( l 2 ), then new length. (l₁=l+ l 2 = 3 l 2 ) ( ) New potential gradient, (K^ = V 3 l 2 K^ = 2 V 3 l ) If (l^ ) be the new balancing length, ( gathered then, E=K^ l^ (iii) or E= 2 V 3 l l^ 2 V 3 l l^ = V 3 l^ = l 2 [ From Eq. (iiii)