The value of the resistance $R$ in the figure is .......... $\Omega$.

Find the equivalent resistance between points $A$ and $B$ for the network shown in the figure.

Find the current flowing through the resistance $R_1$ of the circuit shown in the figure,if the resistances are equal to $R_1=10 \Omega, R_2=20 \Omega$,and $R_3=30 \Omega$,and the potentials of points $1, 2$,and $3$ are equal to $\phi_1=10 \text{ V}, \phi_2=6 \text{ V}$,and $\phi_3=5 \text{ V}$. (in $\text{ A}$)

The figure shows a network of five resistances and two batteries. The current through the $15\,V$ battery is .............. $A$.

Five resistances are connected as shown in the figure. The effective resistance between the points $A$ and $B$ is

In a Wheatstone's bridge,three resistances $P, Q$ and $R$ are connected in the three arms,and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced will be