Capacitive and inductive reactance:
how capacitors and inductors resist AC

Reactance in AC circuits

A resistor opposes current the same way at any frequency. Capacitors and inductors do not. Their opposition, called reactance and measured in ohms, depends on how fast the signal alternates. Unlike resistance it does not turn energy into heat; it stores and returns it each cycle.

A capacitor blocks steady DC and passes fast changes easily. An inductor does the opposite: it lets DC through and resists rapid change. That behaviour is the foundation of filters, tuners and power-line chokes.

Xc and Xl formulas with a worked example

Convert units first. Microfarads and millihenries are the main source of off-by-a-thousand errors.

Prefixes that cause thousand-fold errors

Component values are written with small prefixes, and the formulas expect farads, henries and hertz. Convert before you calculate.

Because Xc depends on the inverse of capacitance, a mistake of a thousand in C gives an answer a thousand times too large or small, while the same slip in L pushes Xl the other way. A plausibility check helps: a 1 µF capacitor should look like a few kilohms at mains frequency and tens of ohms at audio frequencies.

How reactance changes with frequency

Each tenfold rise in frequency makes the capacitor ten times easier to pass and the inductor ten times harder. Notice that the two curves cross somewhere between 50 Hz and 1 kHz, which brings us to resonance.

Where they cancel: resonant frequency

In a series LC circuit the two reactances act in opposite directions, so at one frequency they are equal and the net reactance is zero. That is the resonant frequency.

At that frequency, both reactances equal about 316 Ω. This is how radio tuners and notch filters choose the signal they favour.

Phase, and what to remember when using the numbers

• In a capacitor, current leads voltage by 90 degrees; in an inductor, current lags voltage by 90 degrees.
• Reactance and resistance do not add directly. Combine them as impedance: Z = √(R² + X²) for a series pair, where X = Xl − Xc.
• Ideal parts store energy and return it, so they dissipate no real power; real components have some resistance and loss.
• Values are only valid at the frequency used. A non-sinusoidal signal has several frequencies and each sees a different reactance.

Picking a capacitor for a target reactance

Designers often work backwards from the reactance they want. Rearranging gives C = 1 ÷ (2π × f × Xc). To present about 10 Ω at 100 Hz you need 1 ÷ (2π × 100 × 10) = 159 µF. For 10 Ω at 20 Hz it rises to 796 µF, which is why low-frequency bypass parts are so large.

A coupling capacitor feeding a 10 kΩ input forms a high-pass filter with cutoff 1 ÷ (2π × R × C). With 1 µF that is 1 ÷ (2π × 10,000 × 0.000001) = 15.9 Hz, which keeps most audio and blocks DC and very low rumble.

A full series branch: R, L and C together

Put 100 Ω, 100 mH and 1 µF in series and drive it at 1 kHz. The inductor gives 628.3 Ω and the capacitor 159.2 Ω, and since they oppose, the net reactance is X = 628.3 − 159.2 = 469.2 Ω.

At the resonant frequency of about 503 Hz the reactive parts cancel, Z falls to just R = 100 Ω, and the current climbs to 100 mA. That sharp rise is how a resonant circuit picks out one frequency.

Two places the numbers get used

Power-factor correction is a direct application. A motor or transformer presents inductive reactance, so the current lags the voltage and the supply carries extra current that does no useful work. A parallel capacitor supplies a reactive current of the opposite sense. To cancel an inductive reactance of 20 Ω at 50 Hz, choose Xc = 20 Ω, so C = 1 ÷ (2π × 50 × 20) = 159 µF.

Loudspeaker crossovers are another. A series inductor in front of an 8 Ω woofer forms a low-pass filter: a 2.2 mH coil has Xl = 2π × 1,000 × 0.0022 = 13.8 Ω at 1 kHz, which is already larger than the speaker's own impedance, so higher frequencies are attenuated. A capacitor in series with a tweeter does the opposite.

In both cases reactance is calculated at the frequency of interest, and the real behaviour also depends on the resistance in the circuit and on how close the components are to ideal.

As a closing check, remember that real parts depart from the ideal. A capacitor has some series resistance and inductance of its own, so above a certain frequency it stops behaving like a capacitor, and an inductor has winding resistance and a small parallel capacitance. The formulas on this page hold well in the range these parts are designed for, and datasheets state where they stop being a good model.