Explain the behavior of capacitors and inductors in AC circuits at different frequencies.

Capacitors:

Low frequencies (DC): At DC (0 Hz), a capacitor behaves as an open circuit, effectively blocking the flow of current. It charges up to the voltage applied across it, and once fully charged, no current flows through the capacitor.

Intermediate frequencies: As the frequency increases, the capacitor starts to pass some AC current while still blocking DC. The amount of current that passes depends on the capacitance value and the frequency of the AC signal. Capacitors have a reactance (opposition to AC current) inversely proportional to the frequency, given by the formula: Xc = 1 / (2πfC), where Xc is the capacitive reactance, f is the frequency, and C is the capacitance in Farads.

High frequencies: At very high frequencies, the capacitive reactance becomes very small, allowing a significant amount of current to flow through the capacitor. It acts like a short circuit for AC signals, and the voltage across the capacitor lags the current by 90 degrees in a purely capacitive circuit.

Inductors:

Low frequencies (DC): At DC, an inductor behaves as a short circuit, allowing maximum current flow. The current builds up gradually over time as the magnetic field around the inductor increases.

Intermediate frequencies: As the frequency increases, the inductor's reactance also increases linearly with the frequency. The reactance of an inductor (in ohms) is given by: XL = 2πfL, where XL is the inductive reactance, f is the frequency, and L is the inductance in Henrys. Inductors start to oppose the flow of AC current and pass DC without any impedance.

High frequencies: At very high frequencies, the inductive reactance becomes very large, effectively blocking AC current. Inductors act like open circuits for AC signals, and the voltage across the inductor leads the current by 90 degrees in a purely inductive circuit.

In summary, the behavior of capacitors and inductors in AC circuits depends on the frequency of the AC signal. Capacitors block DC and allow AC to pass, behaving like open circuits at high frequencies and short circuits at low frequencies. Inductors allow DC to pass while blocking AC, behaving like short circuits at low frequencies and open circuits at high frequencies. The transition between these behaviors happens in the intermediate frequency range. The reactance of capacitors decreases with increasing frequency, while the reactance of inductors increases with frequency.