Figure shows a potentiometer wire AB having resistance of $5\ \Omega$ and length 10 m. An e.m.f. is $0.4$ V of battery, the balancing length AP is (internal resistance is negligible)

The currents in different parts of the electric circuit are shown in following figure. The value of current $i$ is

In meter bridge experiment, two resistances X and Y in the two gaps give a null point dividing the wire in the ratio $2 : 3$. When each resistance is increased by $30\,\Omega$, the null point divides the wire in the ratio $5 : 6$. The resistance X and Y are respectively

Two cells of e.m.f. $E_1$ and $E_2$ ($E_1 > E_2$) are connected as shown in figure.

When a potentiometer is connected between points A and B the balancing length of potentiometer wire is $412$ cm. When same potentiometer wire is connected between points A and C the balancing length is $103$ cm. The ratio $E_1 : E_2$ is