A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point $P$. The null point changed to 50 cm from the point $P$, when $16 \Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ are $\_\_\_\_$ .

Two known resistances of $R\ \Omega$ and $2R\ \Omega$ and one unknown resistance $X\ \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points $A$ and $B$ in the circuit is $X\ \Omega$, then the value of $X$ is __________ $\Omega$.

The total length of potentiometer wire AB is 50 cm in the arrangement as shown in the figure. If P is the point where the galvanometer shows zero reading then the length AP is ________ cm.

A battery with EMF $E$ and internal resistance $r$ is connected across a resistance $R$. The power consumption in $R$ will be maximum when: