AC circuits and impedance

On direct current a capacitor is a dead end: charge builds on the plates and flow stops. On alternating current nothing gets to settle. The supply reverses, the plates discharge and recharge the other way, and charge keeps sloshing back and forth through the wires — a real, measurable current, even though no charge crosses the gap. Raise the frequency and the reversals come faster, so more charge moves per second and the capacitor opposes the current less. An inductor does the opposite, opposing changes in current and so obstructing high frequencies most.

This frequency-dependent opposition is called reactance, and it differs from resistance in a way that matters. A resistor's voltage peaks exactly when its current peaks. A capacitor's voltage lags a quarter of a cycle behind its current, an inductor's leads by a quarter cycle. So when a resistor and a reactive component share a circuit, their peak oppositions occur at different moments and cannot simply be added up.

Impedance is the quantity that handles this properly, combining resistance and reactance at right angles — for a series RL circuit, Z = √(R² + X_L²), not R + X_L. The right-angle combination also produces a phase difference between the circuit's overall current and voltage, which is why AC power depends on a power factor rather than just volts times amps. And because capacitive and inductive reactances move oppositely with frequency, they cancel at one particular frequency: that is resonance, and it is what lets a radio pick one station out of the whole band.