In the circuit shown in figure, find the potentials of $A,B,C$ and $D$ and the current through $1\Omega$ and $2\Omega$ resistance.

$V_A=0V$ (as it is earthed)

$V_C-V_A=5V$

$V_C=5V$

$V_B-V_A=2V$

$V_B=2V$

$V_D-V_C=10V$

$V_D=10+V_C=15V$

$i_{1\Omega }=\frac{V_C-V_B}{1}=3A\text{ from }C\text{ to }B\text{ as }{V}_C>V_B$

$i_{2\Omega }=\frac{V_D-V_A}{2}=7.5A\text{ from }D\text{ to }A\text{ as }{V}_D>V_A$