Final answer:
In a DC circuit, a capacitor has infinite impedance and behaves like an open circuit, not allowing DC current to pass once it's charged. In contrast, in an AC circuit, the capacitor charges and discharges with the voltage, allowing for an RMS current to flow. The capacitive reactance is inversely related to the frequency, with high reactance at DC and low reactance at high frequencies.
Step-by-step explanation:
A capacitor is fundamentally an open circuit to direct current (DC). When DC voltage is applied to a capacitor, it charges to that voltage and then no more current flows. This occurs because in a DC circuit, the frequency of the voltage is zero, meaning the current has no path to continue flowing once the capacitor is fully charged. Consequently, the impedance of a capacitor at DC is effectively infinite, which makes the capacitor behave like an open circuit, impeding any DC current.
However, in an alternating current (AC) circuit, the situation is quite different. The voltage in an AC circuit reverses direction periodically, allowing the capacitor to charge and discharge continuously, thereby allowing an RMS current to flow. The reactance of a capacitor, which is the opposition to the change in current, depends on the frequency of the AC voltage. With higher frequencies, the reactance decreases, whereas at lower frequencies, including the zero frequency of DC, the reactance increases.
At very high frequencies, a capacitor's reactance approaches zero, and it offers hardly any opposition to the flow of current, much like a simple conductor. The effect that capacitors have on AC circuits are opposite of that which inductors exhibit. As frequency increases, the impedance of the inductor increases, while that of a capacitor decreases. This difference is essential in designing circuits for specific electronic applications such as filters and oscillators.
When discussing resistors, unlike capacitors and inductors, their impedance does not depend on frequency. A resistor in an AC circuit has the same behavior as in a DC circuit, creating a phase where voltage and current are directly in line, with no reactive property affecting their relationship.