Question

Assuming that the capacitors are uncharged initially, find the charge on each capacitor in steady state.

Answer 1

In steady state current through the capacitor is zero. The two resistors are in series and the equivalent resistance is $9\Omega$. Current through the combination is $i=\frac{V}{R}=\frac{9V}{9\Omega }=1A$
The potential across $3\Omega$ resistor $=1A\times 3\Omega =3V$
This is the potential across the $3\mu F$ capacitor.
So charge in the $3\mu F$ capacitor is $Q=CV=3\mu F\times 3V=9\mu C$
Similarly, potential across $6\Omega$ is 6 V and this is available across $6\mu F$ capacitor.
So charge in the $6\mu F$ capacitor is $Q=CV=6\mu F\times 6V=36\mu C$