Resonant frequency in series circuits
A series RLC circuit containing resistor, inductor, and capacitor exhibits resonance at a specific frequency determined by the inductance and capacitance values. At this resonant frequency, the inductive and capacitive reactances cancel each other, leaving only resistance to limit current. Below resonance, capacitance dominates and impedes current. Above resonance, inductance dominates and impedes current. At resonance, current reaches its maximum for a given voltage. The resonant frequency equals one divided by two-pi times the square root of the product of inductance and capacitance. The sharpness of the resonance peak depends on resistance: low resistance produces a narrow peak where current can become very large, while high resistance produces a broad peak with modest current enhancement.
Practical use in filtering and signal selection
RLC resonance is the principle behind radio tuning circuits, where inductance and capacitance are adjusted to select a specific broadcast frequency. At resonance, energy transfer from the source to the circuit is maximized, making reception efficient. Bandwidth, the range of frequencies where current remains high, depends on the quality factor (Q), which reflects the ratio of energy stored to energy dissipated per cycle. High-Q circuits are narrow and selective, ideal for picking out one radio station. Low-Q circuits are broad and responsive across wide frequency ranges. Audio amplifiers use RLC networks to shape frequency response. Power supplies use resonant circuits to convert and regulate voltage. The design challenge involves balancing selectivity (narrow bandwidth) with the ability to withstand component variations and temperature changes.