State the working principle of potentiometer explain with the help of circuit diagram how the emf of two primary cells are compared by using the potentiometer.

Explanation

working principle of potendiometer : The potential difference across a length of the potentiometer wire is directly proportional to its length (or) when a steady current is passed through a unifrom wire, potential drop per unit length of potential gradient is constant.
ie., `epsilon prop l implies E = phi l` where `phi` is potential gradient.
Comparing the emf of two cell `epsilon_(1)` and `epsilon_(2)` :
(1) To compare the emf of two cells of emf `E_(1)` and `E_(2)` with potentiometer is shown in diagram.

(2) The points marked 1,2,3 form a two way key.
(3) Consider first a position of the key where 1 and 3 are connected so that the galvanometer is connected to `epsilon_(1)`.
(4) The jockey is moved along the wire till at a point `N_(1)` at a distance `l_(1)` from A, there is no deflection in the galvanometer. Then `epsilon_(1) prop l_(1) implies epsilon_(1) = phi l_(1)` .......(1)
(5) similarly, if another emf `epsilon_(2)` is balanced against
`l_(2) (AN_(2))`, them `epsilon_(2) prop l_(2) implies epsilon_(2) = phi l_(2)` ......(2)
(6) `((1))/((2)) implies (epsilon_(1))/(epsilon_(2)) = (l_(1))/(l_(2))`