A null point is obtained at 200 cm on potentiometer wire when cell in secondary circuit is shunted by 5 . When a resistance of 15 is used for shunting, null point moves to 300 cm . The internal resistance of the cell is

Step-by-step solution

The electromotive force (EMF) of the cell is E and the internal resistance is r . When shunted by an external resistance R , the terminal potential difference is V = E R R + r . The potentiometer principle gives V = kL , where k is the potential gradient and L is the balancing length. For R₁ = 5 and L₁ = 200 cm : k 200 = 5E 5 + r For R₂ = 15 and L₂ = 300 cm : k 300 = 15E 15 + r Dividing the first equation by the second: 200 300 = 5E 5 + r 15E 15 + r 2 3 = 5 15 15 + r 5 + r = 1 3 15 + r 5 + r Multiply both sides by