A potentiometer wire of length $L$ and a resistance $r$ are connected in series with a battery of e.m.f. ${\mathrm{E}}_0$ and a resistance ${\mathrm{r}}_1$ . 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:

• Correct answer
  A

  $\frac{{\mathrm{E}}_0\mathrm{r}}{\left(\mathrm{r}+{\mathrm{r}}_1\right)}.\frac{l}{\mathrm{L}}$
• B

  $\frac{{\mathrm{E}}_{0}l}{\mathrm{L}}$
• C

  $\frac{\mathrm{L}{\mathrm{E}}_0\mathrm{r}}{\left(\mathrm{r}+{\mathrm{r}}_1\right)l}$
• D

  $\frac{\mathrm{L}{\mathrm{E}}_0\mathrm{r}}{l\mathrm{ }{\mathrm{r}}_1}$

Hence, the correct answer is option: 'A'.