AC Circuit Design Calculator

When to Use Each Variable

• Solve for Reactance — when you know the frequency and the component value (inductance or capacitance), e.g., finding the opposition a 10 mH inductor presents at 60 Hz.
• Solve for Frequency — when you need the frequency that produces a specific reactance, e.g., tuning an LC filter to resonate at a target impedance.
• Solve for Inductance — when you know the reactance and frequency and need to select an inductor, e.g., choosing a choke for a power supply filter.
• Solve for Capacitance — when you know the reactance and frequency and need to select a capacitor, e.g., sizing a coupling capacitor for an audio crossover.

Key Concepts

Reactance is measured in ohms like resistance, but it shifts the phase between voltage and current rather than dissipating energy. Inductive reactance grows linearly with frequency, while capacitive reactance shrinks inversely. When both are present, they partially cancel: the net reactance is X = X_L − X_C, and at resonance (X_L = X_C) the circuit behaves as a pure resistance.

Applications

• Power systems: sizing capacitor banks for power factor correction on industrial motors
• Audio engineering: designing crossover networks that split signals between woofers and tweeters
• RF design: tuning LC tank circuits to select a specific radio frequency
• Signal filtering: calculating cutoff frequencies for low-pass and high-pass RC/RL filters

Common Mistakes

• Forgetting to convert units — inductance must be in henries and capacitance in farads, not millihenries or microfarads, before plugging into the formula
• Confusing reactance with impedance — reactance is the imaginary component only; impedance combines both resistance and reactance as Z = sqrt(R^2 + X^2)
• Using DC resistance values for AC analysis — at non-zero frequency, inductors and capacitors contribute reactance that pure resistance calculations ignore