Determine the charges on the three capacitors connected to a...

From the given circuit diagram, it can be observed that all three capacitors $C_1$, $C_2$, and $C_3$ are connected in parallel across the battery $V$.

In a parallel circuit, the potential difference across each component is the same. Therefore, the voltage across each capacitor is equal to the battery voltage, $V = 12 \text{ V}$.

The charge on a capacitor is given by the formula $Q = CV$.

For capacitor $C_1$:
$Q_1 = C_1 V = 2.0 \mu\text{F} \times 12 \text{ V} = 24 \mu\text{C}$

For capacitor $C_2$:
$Q_2 = C_2 V = 4.0 \mu\text{F} \times 12 \text{ V} = 48 \mu\text{C}$

For capacitor $C_3$:
$Q_3 = C_3 V = 6.0 \mu\text{F} \times 12 \text{ V} = 72 \mu\text{C}$