Determine the charge on the capacitor depicted in the accompanying...

In steady state, the capacitor acts as an open circuit. The current flows only through the series combination of the resistors.

The equivalent resistance of the circuit is:
$R_{eq} = 10 \Omega + 20 \Omega = 30 \Omega$

The current in the circuit is:
$I = \dfrac{V}{R_{eq}} = \dfrac{2}{30} = \dfrac{1}{15} \text{ A}$

The voltage across the capacitor is equal to the potential difference across the $10 \Omega$ resistor:
$V_C = I \times 10 = \dfrac{1}{15} \times 10 = \dfrac{2}{3} \text{ V}$

The charge on the capacitor is:
$Q = C V_C = 6 \mu\text{F} \times \dfrac{2}{3} \text{ V} = 4 \mu\text{C}$