A potentiometer wire of length \( \mathrm{L} \) and a resistance \( \mathrm{r} \) are connected ...

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A potentiometer wire of length \( \mathrm{L} \) and a resistance \( \mathrm{r} \) are connected in series with a battery of e.m.f. \( \mathrm{E}_{0} \) and a resistance \( r_{1} \). An unknown e.m.f. \( E \) is balanced at a length 1 of the potentiometer wire. The e.m.f. E will be given by:
a. \( \frac{\mathrm{LE}_{0} \mathrm{r}}{\left(\mathrm{r}+\mathrm{r}_{1}\right) \ell} \)
b. \( \frac{\mathrm{LE}_{0} \mathrm{r}}{\ell \mathrm{r}_{2}} \)
c. \( \frac{E_{0} r}{\left(r+r_{1}\right)} \cdot \frac{\ell}{L} \)
d. \( \frac{E_{0} \ell}{L} \)
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