For the arrangement of the potentiometer shown in the figure, The balance point is obtained at a distance `75 cm` from `A` when the key `k` is open
The second balance point is obtained at `60 cm` from `A` when the key `k` is closed. Find the internal resistance of the battery `E_(1)`.

Options

A. `1.5 Omega`
B. `2 Omega`
C. `0.5 Omega`
D. `1 Omega`

Answer

A

Explanation

(a) Let `lambda` is resistance per unit length of wire `AB`. When `k` is opened, `I (lambda x 1) = E_(1)`
After is closed : `I lambda x_(2) = E_(1) - ir`
`i= (E_(1))/(R + r)`
`r = ((X_(1))/(X_(2)) - 1) R ((0.75)/(0.60) - 1) = 6 = 1.5 Omega`