Twelve resistors each of resistance $r$ are joined to form a cube as shown in the figure given below. Find the equivalent resistance between the diagonally opposite points $A$ and $F$.

Given here is a circuit in which ${\epsilon }_1=2.1\mathrm{V}, {\epsilon }_2=1.9\mathrm{V}, R_1=R_2=10\mathrm{\Omega }$ and $R_3=45\mathrm{\Omega }$. Calculate the current in $R_2$ and $R_3$. Neglect the internal resistance of the batteries.

In the circuit given below ${\epsilon }_1={\epsilon }_2=2V, r_1=1\Omega , r_2=2\Omega$ and $I_1=1A$. Find $R, I_2$ and $I_3$ in the circuit.

Find the equivalent resistance between the points $A$ and $B$.

Find the equivalent resistance of the network given below between the points $A$ and $B$.

Find the effective resistance between the points $P$ and $Q$ in the figure given below.