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), the jockey is adjusted to touch the wire at point $$J_1$$ so that there is no deflection in the galvanometer. Now the first battery ($$E_1$$) is replaced by second battery ($$E_2$$) for working by making $$K_1$$ open and $$K_2$$ closed. The galvanometer gives then null deflection at $$J_2$$. The value of $$\frac{E_1}{E_2}$$ is $$\frac{a}{2}$$, where $$a$$ = ______.