A Potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of emf $E_0$ and a resistance $r_1$. An unknown emf E is balanced at a length $l$ of the potentiometer wire. The emf E will be:

$\frac{LE_0 r}{\left(r+r_1\right) l}$ $\frac{E_0 r}{l r_1}$ $\frac{E_0 r}{\left(r+r_1\right)} . \frac{l}{L}$ $\frac{E_0 l}{L}$

$\frac{E_0 r}{\left(r+r_1\right)} . \frac{l}{L}$

$ I = \frac{E_0}{r+r_1}$ $ E = I \times \frac{l r}{L} = \frac{E_0 r}{r+r_1} \frac{l}{L}$