In potentiometer experiment, if `l_(1)` is the balancing length for e.m.f. of the cell of internal resistance r and `l_(2)` is the balancing length for its terminal potential difference when shunted with resistance R then :

Options

A. `l_(1) = l_(2) ((R + R)/(R ))`
B. `l_(1) = l_(2) ((R )/(R - r))`
C. `l_(1) = l_(2) ((R )/(R + r))`
D. `l_(1) = l_(2) ((R - r)/(R ))`

Answer

a

Explanation

`l_(1) = l_(2)((R + r)/(R ))`
The internal resistance of a cell is given a
`r = ((l_(1) - l_(2))/(l_(2)))R`
`r/R = (l_(1) - l_(2))/(l_(2))`
`:. rl_(2) = Rl_(1) - Rl_(2)`
`:. l_(2) (R + r) = Rl_(1)`
`:. l_(1) = l_(2) ((R + r))/(R)`