RLC Impedance Calculator

RLC Impedance in AC Circuits

In alternating current, inductors and capacitors oppose current flow through reactance. Combined with resistance, the total opposition to current is impedance Z, a complex quantity with magnitude and phase.

Impedance Formula

$$X_L = 2\pi f L, \quad X_C = \frac{1}{2\pi f C}$$ $$|Z| = \sqrt{R^2 + (X_L - X_C)^2}, \quad \phi = \mathrm{atan2}(X_L - X_C, R)$$

When $X_L > X_C$ the circuit is inductive and current lags voltage. When $X_C > X_L$ it is capacitive and current leads voltage. At resonance $X_L = X_C$ and impedance equals R.

Reading Phase Angle

Phase $\phi$ is the angle by which voltage leads current in a series branch. Positive phase means inductive behavior. Negative phase means capacitive behavior.

Frequently Asked Questions

What is the difference between reactance and impedance?

Reactance comes only from L or C. Impedance combines resistance and net reactance: |Z| = √(R² + X²).

When is impedance equal to resistance?

When inductive and capacitive reactances cancel so X_L = X_C. Then |Z| = R and phase angle is zero.

Why does frequency affect impedance?

X_L grows with frequency while X_C shrinks. Changing f shifts the balance between inductive and capacitive effects.

What units does this calculator expect?

Resistance in ohms, inductance in millihenries, capacitance in microfarads, and frequency in hertz.

Can impedance be less than resistance?

No for a series RLC branch. |Z| is always at least R because reactance adds in quadrature with resistance.

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RLC Impedance Calculator

RLC Impedance in AC Circuits

Impedance Formula

Reading Phase Angle

Frequently Asked Questions

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