Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.

Explanation

POTENTIOMETER : A potentiometer is a device used to measure potential difference :
Principle : When a current flows thorugh a wire of uniform thickness, the potential difference between its two points is directly proportional to the length of the wire between these two points.

where K is called construction potential gradient.
Determination of internal resistance of a cell : The cell (emf `epsilon`)whose internal resistance (r) is to be determined, is connected across a resistance box through a key `K_2` as shown in figure.
With key `K_2`, open, balance in obtained at
length `l_1(AN_1)`. Then,
`epsilon =phi l_1 .............(i)`
where `phi` is the potential drop per unit length.
When key `K_2`, is closed, the cell sends a current (I) through the resistance box (R). if V is the terminal potential difference of the cell and balance is obtained at length `l_2(AN_2)`.
` therefore V=phi l_2`
Dividing (i) by (ii), we get
` (epsilon)/(V)=(phi l_1)/(phil_2)=(l_1)/(l_2) ...............(iii)`
But ` epsilon =I(r+R) and V=IR`
`(I(r+R))/(IR) =(I_1)/(l_2)rArr (r+R)/(R)=(I_1)/(I_2)`
`(r)/(R)+(R)/(R)=(I_1)/(1_2)rArr (r)/(R0((I_1)/(I_2)-1)`
`therefore r= R((I_1)/(I_2)-1) .........(iv)`
Using equation (iv), we can find the internal resistance of the given cell.