RLC Circuit Theory

An RLC circuit contains a resistor (R), an inductor (L) and a capacitor (C). These three passive components behave very differently when an alternating current flows through them, and their combination produces some of the most important effects in electronics, including filtering, tuning and resonance. The resistor dissipates energy as heat, the inductor stores energy in a magnetic field, and the capacitor stores energy in an electric field. The interplay between energy storage and exchange between the inductor and capacitor gives RLC circuits their characteristic behaviour.

In an AC circuit, the inductor and capacitor oppose current through reactance, which depends on frequency. Inductive reactance rises with frequency, while capacitive reactance falls with frequency. Combined with resistance, these form the impedance, the total opposition to alternating current, which has both a magnitude and a phase. Because the inductor and capacitor shift the phase between voltage and current in opposite directions, their effects partly cancel, and the overall phase and amplitude of the current depend strongly on the driving frequency.

At one particular frequency, the resonant frequency, the inductive and capacitive reactances are equal and cancel exactly, leaving only the resistance. At resonance a series RLC circuit has minimum impedance and maximum current, while a parallel RLC circuit has maximum impedance. This sharp frequency dependence makes RLC circuits ideal for selecting or rejecting particular frequencies, as in radio tuners and filters. The sharpness of the response is described by the quality factor, or Q, with higher Q giving a narrower, more selective peak. Transient analysis shows that, depending on the resistance, the circuit can be underdamped and oscillate, critically damped, or overdamped and return slowly to rest.

Frequently asked questions

What is resonance in an RLC circuit?

The condition where inductive and capacitive reactances are equal and cancel, leaving only resistance. A series circuit then has minimum impedance and maximum current.

What is impedance?

The total opposition an AC circuit presents to current, combining resistance and reactance. It has both a magnitude and a phase angle between voltage and current.

What does the quality factor Q describe?

How sharply a resonant circuit responds around its resonant frequency. Higher Q means a narrower, more selective bandwidth and lower energy loss per cycle.