Determine the charges on the three capacitors connected to a battery as depicted in the figure. Assume C₁ = 2.0 F , C₂ = 4.0 F , C₃ = 6.0 F , and V = 12 volts.

Step-by-step solution

From the given circuit diagram, it can be observed that all three capacitors C₁ , C₂ , and C₃ 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 V . The charge on a capacitor is given by the formula Q = CV . For capacitor C₁ : Q₁ = C₁ V = 2.0 F 12 V = 24 C For capacitor C₂ : Q₂ = C₂ V = 4.0 F 12 V = 48 C For capacitor C₃ : Q₃ = C₃ V = 6.0 F 12 V = 72 C