State the working principle of potentiometer explain with the help of circuit diagram how the potentiometer is used to determine the internal resistance of the given primary cell.

Explanation

Working principle of potentiometer : 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 uniform wire, potential drop per unit length or potential gradient is constant.
ie., `epsilon prop l implies epsilon = phi l` ,
where `phi` is potential gradient.
Measurement of internal resistance (r ) with potentiometer :
(1) Potentiometer to measure internal resistance (r ) of a cell `(epsilon)` is shown in diagram.
(2) The cell (emf `espilon`) whose internal resistance (r ) is to be determined is connected across a resistance box (R.B) through a key `K_(2)`.
(3) With key `K_(2)` open, balance is obtained at length `l_(1)(AN_(1))`. Then `epsilon = phi l_(1) to (1)`
(4) When key `k_(2)` is closed, the cell sends a current (I) through the resistance box (R.B)
(5) If V is the terminal potential difference of the cell and balance is obtined at length `l_(2) (AN_(2))`
Then `V = phi l_(2) to (2)`
(6) `((1))/((2)) implies (epsilon)/(V) = (l_(1))/(l_(2)) to (3)`
(7) But `epsilon = I (r + R)` and V = IR. This gives
`(epsilon)/(V) = ((r + R))/(R )`
`(l_(1))/(l_(2)) = (r )/(R ) + 1) [ :' "from" (3)]`
`:. r = R ((l_(1))/(l_(2)) - 1)`
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