In the given circuit of potentiometer, the potential difference E across AB ( 10 m length) is larger than E_1 and E_2 as well. For key K_1 (closed),…

In the given circuit of potentiometer, the potential difference E across AB ( $\displaystyle 10$ m length) is larger than $\displaystyle \mathrm{E}_1$ and $\displaystyle \mathrm{E}_2$ as well. For key $\displaystyle \mathrm{K}_1$ (closed), the jockey is adjusted to touch the wire at point $\displaystyle \mathrm{J}_1$ so that there is no deflection in the galvanometer. Now the first battery $\displaystyle \left(\mathrm{E}_1\right)$ is replaced by second battery $\displaystyle \left(\mathrm{E}_2\right)$ for working by making $\displaystyle \mathrm{K}_1$ open and $\displaystyle \mathrm{K}_2$ closed. The galvanometer gives then null deflection at $\displaystyle \mathrm{J}_2$. The value of $\displaystyle \frac{\mathrm{E}_1}{\mathrm{E}_2}$ is $\displaystyle \frac{\mathrm{a}}{\mathrm{b}}$, where $\displaystyle \mathrm{a}=$ \_\_\_\_.