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

Answer

C

Explanation

Current in wire `AB=(E_(0))/(r_(1)+r)`
Potential gradient`=((E_(0))/(r_(1)+r))*(r)/(L)`
`thereforeE=((E_(0))/(r_(1)+r))(r)/(L)xxl`