RLC Impedance Calculator

About the RLC Impedance Calculator

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.

When This Page Helps

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.

How to Use the Inputs

1. Choose input mode: enter reactances directly or specify L, C, and frequency to auto-calculate reactances.
2. Enter the resistance R in ohms.
3. Enter inductive reactance X_L and capacitive reactance X_C (or L, C, frequency in component mode).
4. Enter the applied voltage to compute current and power quantities.
5. Review impedance, phase, current, and power factor in the output cards.
6. Examine the impedance triangle visualization to see the R, X, Z relationship graphically.
7. Study the voltage and power distribution table for component-level analysis.

Example Calculation

Tips & Best Practices

• When X_L > X_C, the circuit is inductive (positive phase) and current lags voltage. When X_C > X_L, it is capacitive.
• At resonance (X_L = X_C), impedance equals R and the power factor is 1.0 — all power delivered is real power.
• In series RLC circuits, individual component voltages can exceed the source voltage due to voltage magnification.
• Power factor correction adds capacitance to reduce inductive reactance, bringing the power factor closer to unity.
• Use the component input mode when designing circuits; use reactance mode when analyzing measured values.
• The impedance triangle is geometrically similar to the power triangle (P, Q, S).

The Impedance Triangle

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.

Power in AC Circuits

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.

Practical Impedance Matching

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.

Frequently Asked Questions

• What is impedance?

  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.

• What is the impedance at resonance?

  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.

• Why can component voltages exceed the source voltage?

  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.

• What is the difference between real, reactive, and apparent power?

  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).

• How does frequency affect impedance?

  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).

• What is a good power factor?

  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.