Reactance of Capacitors and Inductors: AC Opposition

Resistance is opposition that dissipates energy. Reactance is opposition caused by energy storage. Capacitors store energy in an electric field, inductors store energy in a magnetic field, and both create frequency-dependent opposition to AC current.

Learning Objectives

By the end of this lesson, you should be able to:

• calculate capacitive reactance and inductive reactance;
• predict how reactance changes with frequency;
• explain capacitor and inductor phase behavior;
• identify practical uses in coupling, filtering, and power conversion;
• avoid formula and unit mistakes.

DC and AC Behavior

At steady DC, an ideal capacitor behaves like an open circuit after it charges, while an ideal inductor behaves like a short circuit after current settles.

In AC circuits, voltage and current keep changing. The capacitor must charge and discharge, and the inductor must build and collapse magnetic field energy. That is why frequency matters.

Capacitive Reactance

Capacitive reactance is:

$$
X_C=\frac{1}{2\pi f C}
$$

where X_C is in ohms, f is in hertz, and C is in farads.

As frequency increases, X_C decreases. A capacitor blocks DC, opposes low frequency strongly, and passes high frequency more easily.

Worked example for C = 1 uF:

Inductive Reactance

Inductive reactance is:

$$
X_L=2\pi f L
$$

where X_L is in ohms, f is in hertz, and L is in henries.

As frequency increases, X_L increases. An inductor passes DC easily in the ideal case and opposes high-frequency current changes.

Worked example for L = 100 mH:

Phase Relationship

Reactance also changes the timing between voltage and current.

title "Ideal reactive phase examples"
time start=0 end=20 unit=ms divisions=5

V: sine label="voltage reference" amplitude=1 cycles=1 unit=norm color=#2563eb
IC: sine label="capacitor current leads" amplitude=1 cycles=1 phase=90 unit=norm color=#16a34a
IL: sine label="inductor current lags" amplitude=1 cycles=1 phase=-90 unit=norm color=#dc2626

This waveform is illustrative and normalized.

Reactance Calculator

Applications

Capacitors are used for AC coupling, bypassing, low-pass filters, high-pass filters, timing networks, and switched-mode converter energy transfer. Inductors are used for current smoothing, EMI filters, transformers, tuned circuits, and energy storage in converters.

Real Components

Real capacitors have equivalent series resistance, equivalent series inductance, leakage, voltage coefficient, tolerance, and dielectric limits. Real inductors have winding resistance, saturation current, core loss, self-resonance, and stray capacitance. At high frequency, parasitics can dominate the ideal formula.

Common Mistakes

• Using microfarads or millihenries directly without converting units.
• Writing the inductor formula incorrectly; it is X_L = 2 pi f L.
• Forgetting that reactance is frequency-dependent.
• Assuming ideal 90 deg phase for lossy real components.
• Ignoring capacitor voltage rating or inductor saturation current.

Summary

Capacitive reactance decreases with frequency: X_C = 1/(2 pi f C). Inductive reactance increases with frequency: X_L = 2 pi f L. These two relationships explain AC coupling, filters, resonance, EMI suppression, and many power-conversion behaviors.

Further Reading

• All About Circuits: Reactance and Impedance
• Electronics Tutorials: Capacitive Reactance
• Electronics Tutorials: Inductive Reactance

Mind Map