What is the principle of a potentiometer? With the help pf circuit diagram, explain the use of potentiometer to measure internal resistance of a given primary cell.

Explanation

Principle of Potentiometer: To measure the internal resistance of a cell with the help of potentiometer: The arrangement for measuring the internal resistance (r ) of a cell using potentiometer is shown in the figure.

E= e.m.f of auxiliary battery
I= Constant current flowing through the potentiometer wire
Close to key `K_(1)` by keeping the kye `K_(2)` open. The jockey is moved over the potentiometer wire so as to balance the e.m.f (E ) of the cell, whose internal resistance (r ) is to be found. Let `l_(1) = AJ`= Balancing length of potentiometer wire between point A and jockey J. At this stage, potential difference across A and J is equal to e.m.f (E ) of cell and galvanometer gives no deflection.
So `E= V_(AJ) prop l_(1)`
`or E= Kl_(1)` ...(1)
Now close key `K_(2)` so that the known resistance (R ) is connected across the cell. Find the balance point J., such taht on pressing the Jockey at J, galvanometer gives no deflection. At this stage, terminal potential difference (V) is equal to the potential difference across A and J.
If `AJ= l_(2)` then `V= V_(AJ.) prop l_(2)`
or `V= K l_(2)` ...(2)
Divide (1) by (2),
`(E )/(V)= (Kl_(1))/(Kl_(2))= (l_(1))/(l_(2))`
We know internal resistance `(r )= ((E)/(V) -1) R`
`rArr r= ((l_(1))/(l_(2))-1) R`
`r= ((l_(1)-l_(2))/(l_(2))) R`
So by knowing the value of `l_(1), l_(2)` and R, we can find the internal resistance of cell.