Calculate RLC circuit impedance Z = √(R² + (X_L − X_C)²), phase angle, current, power factor, and voltage distribution with impedance triangle visualization.
Impedance is the total opposition a circuit presents to alternating current, combining resistance (R) and reactance (X) into a single complex quantity. For a series RLC circuit, the impedance magnitude is Z = √(R² + (X_L − X_C)²), where X_L is the inductive reactance and X_C is the capacitive reactance. The phase angle between voltage and current is φ = arctan((X_L − X_C)/R).
Understanding impedance is crucial for AC circuit design, power system analysis, and RF engineering. Unlike simple DC resistance, impedance varies with frequency because reactance depends on the operating frequency. At resonance (where X_L = X_C), the impedance equals pure resistance, and the power factor reaches unity.
This calculator computes impedance magnitude, phase angle, current flow, power factor, and complete voltage and power distribution. You can enter reactance values directly or specify component values with frequency to compute reactances automatically. The impedance triangle visualization helps you understand the relationship between resistance, reactance, and total impedance.
AC impedance calculations require complex arithmetic — magnitude from Pythagorean theorem, phase from inverse tangent, and power quantities from multiple dependent formulas. This calculator automates the entire chain from input values through impedance, current, voltage drops, and power quantities. The visual impedance triangle and distribution table make it easy to verify and understand results.
Impedance: Z = √(R² + (X_L − X_C)²) φ = arctan((X_L − X_C) / R) Reactances: X_L = 2πfL X_C = 1/(2πfC) Current: I = V / |Z| Power Factor: PF = cos(φ) = R / |Z| Real Power: P = I²R = VI·cos(φ) Reactive Power: Q = I²|X| Apparent Power: S = VI
Result: |Z| = 64.03 Ω at 38.66°
Net reactance X = X_L − X_C = 100 − 60 = 40 Ω (inductive). Impedance |Z| = √(50² + 40²) = √(2500 + 1600) = √4100 ≈ 64.03 Ω. Phase angle φ = arctan(40/50) ≈ 38.66°. Current I = 120/64.03 ≈ 1.874 A. Power factor = cos(38.66°) ≈ 0.781.
The impedance triangle is a right triangle where the horizontal side is resistance R, the vertical side is net reactance X = X_L − X_C, and the hypotenuse is impedance magnitude |Z|. The angle between R and Z is the phase angle φ. This triangle is a powerful visualization tool because it shows at a glance whether a circuit is resistive, inductive, or capacitive, and how close it is to resonance.
Unlike DC circuits where P = VI, AC power has three components. Real power P = VI·cos(φ) represents actual energy consumption. Reactive power Q = VI·sin(φ) represents energy sloshing back and forth between source and reactive components. Apparent power S = VI is what the source must supply. These three form the power triangle, geometrically similar to the impedance triangle.
In RF and audio systems, maximum power transfer occurs when the source impedance equals the complex conjugate of the load impedance. This means matching both resistance and reactance. Impedance matching networks (L-networks, pi-networks, T-networks) use combinations of inductors and capacitors to transform one impedance to another at the operating frequency.
Impedance (Z) is the total opposition an AC circuit presents to current flow. It combines resistance (which dissipates energy) and reactance (which stores and returns energy). Impedance is a complex number measured in ohms.
At resonance, X_L = X_C so they cancel, leaving Z = R. The impedance is purely resistive, the phase angle is zero, and the power factor is 1.0.
In a series RLC circuit, the inductor and capacitor voltages are 180° out of phase. Each can be much larger than the source voltage (by a factor of Q), but their phasor sum partially cancels. The total phasor voltage still equals the source.
Real power (W) is consumed by resistance as heat. Reactive power (var) oscillates between source and reactive components without doing work. Apparent power (VA) is the product V×I and equals √(P² + Q²).
Inductive reactance increases with frequency (X_L = 2πfL) while capacitive reactance decreases (X_C = 1/(2πfC)). Below resonance, X_C dominates (capacitive circuit); above resonance, X_L dominates (inductive circuit).
Power factors above 0.9 are generally considered good. Utilities may charge penalties for power factors below 0.85. Unity (1.0) is ideal, meaning all power delivered is useful real power.