What is the resonant frequency of an RLC circuit?

The resonant frequency of an RLC circuit is f₀ = 1 / (2π√(LC)), where L is inductance in henrys and C is capacitance in farads. At resonance, inductive reactance XL equals capacitive reactance XC, the impedance is purely resistive (Z = R), and the phase angle is zero.

How do you calculate impedance in a series RLC circuit?

In a series RLC circuit, impedance Z = √(R² + (XL − XC)²), where XL = 2πfL is the inductive reactance and XC = 1/(2πfC) is the capacitive reactance. The phase angle is φ = arctan((XL − XC) / R). When XL > XC the circuit is inductive; when XC > XL it is capacitive.

What is the Q factor of an RLC circuit and why does it matter?

The quality factor (Q) measures how sharply an RLC circuit resonates. For a series RLC circuit, Q = (1/R)√(L/C). A higher Q means a narrower bandwidth and sharper resonance peak. Q factor is critical in filter design, radio tuning circuits, and signal processing applications.

RLC Circuit — AC Circuit Analysis

Z = R + j(X_L−X_C) • Impedance • Resonance • Phasors — Simulate • Explore • Practice • Quiz

Mode

Circuit Type

R (Ω) 100 Ω

L (mH) 10.0 mH

C (µF) 10.0 µF

f (Hz) 50 Hz

V_peak (V) 12.0 V

Presets

Impedance Z

100.0 Ω

Phase Angle φ

0.0 °

Current I_rms

84.9 mA

X_L

3.14 Ω

X_C

318.3 Ω

f₀ Resonant

503.3 Hz

Power Factor

1.00

Q Factor

3.16

Understanding RLC Circuits — Free Interactive AC Circuit Simulator

An RLC circuit contains a resistor (R), inductor (L), and capacitor (C) connected to an alternating current (AC) source. It is one of the most important circuits in electrical engineering, forming the basis of filters, oscillators, and tuning circuits. The interplay between inductive reactance X_L = 2πfL and capacitive reactance X_C = 1/(2πfC) determines the circuit’s impedance, phase angle, and frequency response. Our interactive simulator lets you adjust R, L, C, and frequency in real time and observe animated phasor diagrams, sinusoidal waveforms, and all key readouts instantly.

Impedance and Phase Angle in AC Circuits

In a series RLC circuit, the total impedance is Z = √(R² + (X_L−X_C)²). The phase angle between voltage and current is φ = arctan((X_L−X_C)/R). When the circuit is inductive (X_L > X_C), voltage leads current; when capacitive (X_C > X_L), current leads voltage. The simulator displays these relationships through rotating phasor vectors and phase-shifted sine waves so you can see exactly how changing any component affects circuit behaviour.

Resonance — The Special Frequency

Resonance occurs at f₀ = 1/(2π√(LC)), where X_L = X_C. At this frequency, the impedance of a series RLC circuit drops to its minimum value (Z = R), current reaches its maximum, and the phase angle becomes zero. In a parallel RLC circuit, resonance produces maximum impedance instead. Resonance is the principle behind radio tuning, bandpass filters, and many sensor circuits. The simulator highlights the resonant frequency in the readout panel and lets you see the dramatic change in current and phase as you sweep through resonance.

Quality Factor and Bandwidth

The Q factor (quality factor) measures the sharpness of resonance. For a series RLC circuit, Q = (1/R)√(L/C) or equivalently Q = f₀/BW, where BW is the bandwidth between the half-power (−3 dB) points. A high-Q circuit has a narrow bandwidth and strong frequency selectivity, making it ideal for signal filtering. A low-Q circuit has a wide bandwidth and responds to a broader range of frequencies. Adjust R in the simulator to see how damping affects Q and the sharpness of the resonance peak.

Who Uses This Simulator?

This simulator is designed for electrical engineering students, electronics technicians, physics students studying AC circuits, and TVET trainees learning about impedance, resonance, and filter design. It provides visual, hands-on understanding of phasor relationships and frequency response without requiring laboratory equipment or SPICE simulation software.

Explore Related Simulators

If you found this RLC Circuit simulator helpful, explore our Ohm’s Law simulator, RC Circuit simulator, Transformer simulator, Wheatstone Bridge simulator, and Star-Delta Conversion simulator for more hands-on electrical engineering practice.