How does a capacitor behave when connected to a DC power source and an AC power source?

📌 CONCEPT: A capacitor behaves differently when connected to a DC power source and an AC power source due to the change in the nature of the current flowing through it.

📐 RULE / FORMULA: The formula for the reactance of a capacitor is Xc = 1 / (ωC), where ω is the angular frequency of the AC source and C is the capacitance of the capacitor.

💡 WORKED EXAMPLE: Consider a capacitor of capacitance 10 μF connected to an AC power source of frequency 50 Hz. The reactance of the capacitor is Xc = 1 / (2π x 50 x 10 μF) = 318 Ω. This means that the capacitor will oppose the flow of AC current by 318 Ω.

⚠️ COMMON MISTAKE: Students often get confused between the behavior of a capacitor in DC and AC circuits, assuming that a capacitor will behave the same way in both cases. However, the capacitor will behave as a short circuit in a DC circuit, allowing current to flow, whereas in an AC circuit, it behaves as a reactance, opposing the flow of current.