A potentiometer wire of Length `L` and a resistance `r` are connected in series with a battery of e.m.f. `E_(0)` and a resistance `r_(1)`. An unknown e.m.f. `E` is balanced at a length `l` of the potentiometer wire. The e.m.f. `E` will be given by :

Options

A. `(E_(0)r/(r + r_(1))).I/L`
B. `(E_(0)I)/L`
C. `(LE_(0)r)/((r+r_(1))l)`
D. `(LE_(0)r)/(lr_(1))`

Answer

D

Explanation

`i=E_(0)/(r + r_(1))`
`E = (rl)/L (E_(0)/(r + R_(1))) = (E_(0)rl)/((r + r_(1))L)`