RLC Circuit — AC Circuit Analysis

The RLC Circuit Simulator is an interactive tool for analysing alternating current (AC) circuits containing a resistor (R), inductor (L), and capacitor (C). It demonstrates the interplay between impedance, resonance frequency, phasor diagrams, power factor, bandwidth, and Q factor. You can switch between series and parallel RLC configurations, adjust component values and frequency, and watch animated phasor vectors and sinusoidal waveforms update in real time.

This simulator targets electrical engineering students studying AC circuit analysis, electronics technicians working with filters and oscillators, and engineering trainees learning about impedance matching and frequency-selective circuits.

The simulator opens in Simulate mode with a series RLC circuit: R = 100 Ω, L = 10 mH, C = 10 μF, f = 50 Hz, and V_peak = 12 V. To begin experimenting:

• Choose Series RLC or Parallel RLC using the circuit type pills.
• Drag the R, L, C, and f sliders to change component values and frequency. The canvas and readouts update instantly.
• Adjust V_peak to change the AC source amplitude.
• Load a Preset such as Resonance, High-Q Filter, Low-Pass, or Radio Tuner to explore common configurations.

Use the four mode tabs — Simulate, Explore, Practice, Quiz — to progress from hands-on experimentation to structured learning and self-assessment.

Simulate mode is the main interactive workspace. The canvas shows the circuit schematic, rotating phasor diagram, and AC waveforms. Key controls:

• R slider (1–1000 Ω): Sets resistance. Higher R increases damping and lowers the Q factor.
• L slider (0.1–100 mH): Sets inductance. Inductive reactance X_L = 2πfL increases with both inductance and frequency.
• C slider (0.1–100 μF): Sets capacitance. Capacitive reactance X_C = 1/(2πfC) decreases as capacitance or frequency increases.
• f slider (1–1000 Hz): Sets the AC source frequency. Sweep through resonance to see impedance drop to minimum (series) or rise to maximum (parallel).
• V_peak slider (1–24 V): Sets the peak amplitude of the AC source.

The readout cards display: impedance Z, phase angle φ, RMS current I_rms, inductive reactance X_L, capacitive reactance X_C, resonant frequency f₀, power factor cos(φ), and Q factor. Watch the phasor diagram to see voltage leading or lagging current depending on whether the circuit is inductive (X_L > X_C) or capacitive (X_C > X_L).

Explore mode provides structured reference material in three categories:

• AC Fundamentals: Covers sinusoidal waveforms, peak vs RMS values, frequency and period, and the concept of phase angle between voltage and current.
• Impedance & Reactance: Explains inductive reactance (X_L = 2πfL), capacitive reactance (X_C = 1/(2πfC)), total impedance (Z = √(R² + (X_L−X_C)²)), and the impedance triangle.
• Resonance & Power: Describes the resonance condition (f₀ = 1/(2π√(LC))), Q factor (Q = (1/R)√(L/C)), bandwidth (BW = f₀/Q), real and reactive power, and power factor correction.

Select any concept to see its detailed explanation with formulas and an interactive canvas illustration.

Practice mode generates calculation problems on RLC circuits, such as: “Find the impedance of a series RLC circuit with R = 50 Ω, X_L = 80 Ω, X_C = 30 Ω”, “Calculate the resonant frequency for L = 20 mH and C = 5 μF”, or “What is the power factor when φ = 30°?” Enter your answer and receive step-by-step feedback.

Quiz mode tests your knowledge with 5 multiple-choice questions on impedance, resonance, phasors, Q factor, and AC power. Review your results and explanations at the end.

• Use the Resonance preset to see the dramatic effect: impedance drops to R, current peaks, and phase angle becomes zero in a series RLC circuit.
• Slowly sweep the frequency slider through the resonant point and observe how phasor angles transition from capacitive (current leads) to inductive (voltage leads).
• Compare series and parallel RLC behaviour at the same resonant frequency — series gives minimum Z, parallel gives maximum Z.
• Lower R to increase Q factor and narrow the bandwidth. A sharp resonance peak is desirable for radio tuning circuits.
• The power factor equals cos(φ). At resonance, power factor is unity (1.00), meaning all power is real power with no reactive component.
• Remember that X_L increases linearly with frequency while X_C decreases inversely — they must cross at f₀.
• For filter design, the −3 dB bandwidth is centred on f₀ and equals f₀/Q. Higher Q means a narrower passband.