Reactance Calculator

Reactance (X) is the purely imaginary (90-degree out-of-phase) part of impedance - it represents energy storage, not dissipation. Impedance (Z) is the complete complex opposition to current, combining both resistance R (the real, in-phase part that dissipates energy as heat) and reactance X (the imaginary, 90-degree part). The relationship is Z = R + jX for a series circuit, and the magnitude is |Z| = √(R² + X²). A pure inductor has Z = jXL; a pure capacitor has Z = -jXC; a real inductor with winding resistance r has Z = r + jXL. Reactance causes voltage and current to be out of phase; resistance causes them to be in phase.

In phasor (complex number) notation, inductive reactance is assigned a positive imaginary value (+jXL) because the voltage across an inductor leads the current by 90 degrees. Capacitive reactance is negative imaginary (-jXC) because the voltage across a capacitor lags the current by 90 degrees. This sign convention ensures that when a capacitor and inductor are in series, their reactances subtract: Xnet = XL - XC. At resonance they cancel exactly, leaving only the series resistance, and impedance is at its minimum. The convention is not a physical "negative opposition" - it is a bookkeeping tool for tracking phase angles in circuit analysis.

At the resonant frequency f₀ = 1 ÷ (2π√(LC)), the inductive and capacitive reactances are equal in magnitude and opposite in sign, so they cancel: XL = XC and Xnet = 0. For a series RLC circuit, total impedance collapses to just the series resistance R - impedance is at its minimum and current is at its maximum for a given applied voltage. The voltage across the inductor and capacitor can each be Q times larger than the source voltage, which is exploited in bandpass filters and oscillators. For a parallel RLC circuit, behavior is inverted: impedance is maximum at resonance and current from the source is minimum, while large circulating currents flow between L and C internally.

Skin effect is the tendency of high-frequency AC current to flow near the conductor surface rather than through the full cross-section, effectively reducing the conducting area and raising resistance. For a copper conductor the skin depth at 10 kHz is about 0.66 mm; at 1 MHz it shrinks to 0.066 mm. This means a 1 mm diameter copper wire behaves like a much thinner, higher-resistance conductor at radio frequencies - the AC resistance can be five to ten times the DC resistance. Equivalent series resistance (ESR) in capacitors represents a similar effect plus dielectric losses, and causes capacitors to heat under high ripple-current conditions. Both effects lower the Q factor of a resonant circuit and must be measured with an impedance analyzer at the frequency of interest rather than estimated from DC resistance.

A real inductor has parasitic capacitance between its winding turns. This distributed capacitance forms a parallel LC circuit with the inductance itself, creating a self-resonant frequency (SRF) above which the component behaves as a capacitor rather than an inductor. For a typical 10 mH leaded RF choke the SRF might be 5–20 MHz; for a 1 µH surface-mount inductor it might be 200–800 MHz. Operating an inductor above its SRF defeats its purpose - it will have capacitive reactance instead of inductive reactance. SRF is specified on high-frequency inductor data sheets and must be checked when designing RF circuits or high-frequency power converters.