Figure 1: A capacitor’s reactance falls inversely with frequency. At DC (f=0) it acts as an open circuit. At high frequencies it acts as a short circuit.
Enter target Xᴄ and one known value.
Table of Contents
What Is Capacitive Reactance?
Capacitive reactance (XC) is the opposition a capacitor presents to alternating current. It is inversely proportional to both frequency and capacitance: higher frequency or larger capacitance means less opposition. At DC, a capacitor is an open circuit (infinite reactance); at very high frequencies it approaches a short circuit (near-zero reactance).
Like inductive reactance, capacitive reactance is measured in ohms but causes a phase shift — current leads voltage by 90°. This is the opposite of an inductor where current lags voltage. The Inductive Reactance Calculator computes the complementary XL value.
The Formula
Where f = frequency (Hz), C = capacitance (farads), ω = angular frequency (rad/s).
Impedance of a pure capacitor: Z = −jXC (purely imaginary, −90° phase)
Worked Example — Coupling Capacitor at 1 kHz
Step 1 — ω = 2π × 1000 = 6283 rad/s
Step 2 — XC = 1/(6283 × 100×10−9) = 1591.5 Ω
At 1 kHz this 100 nF capacitor has high reactance — it will significantly attenuate the signal. For audio coupling where you want the capacitor to be nearly transparent, you would need a much larger capacitance or a lower target frequency.
Worked Example — Power Supply Filter at 50 Hz
Step 1 — XC = 1/(2π × 100 × 1000×10−6) = 1.59 Ω
The low reactance at 100 Hz means this capacitor effectively short-circuits the ripple voltage to ground, smoothing the DC output. The RMS Voltage Calculator can help determine the ripple voltage magnitude.
Worked Example — RF Bypass at 100 MHz
Step 1 — XC = 1/(2π × 100×106 × 100×10−12) = 15.92 Ω
Even a tiny 100 pF capacitor provides low reactance at RF frequencies, making it effective as a bypass or decoupling capacitor. At these frequencies, the capacitor’s parasitic inductance (ESL) becomes significant and may limit its effectiveness above its self-resonant frequency.
How Frequency Affects XC
Capacitive reactance is inversely proportional to frequency. On a log-log graph, XC vs frequency is a straight line with a slope of −1 decade/decade (−20 dB/decade). This is the mirror image of inductive reactance, which has a +1 slope. The two lines cross at the resonant frequency, where XL = XC.
Phase Relationship
In a pure capacitor, current leads voltage by exactly 90°. The mnemonic “ELI the ICE man” helps: in an I-C-E circuit, I (current) leads E (voltage). The Phase Angle Calculator shows how this phase shift combines with resistance in practical RC circuits.
Common Applications
Capacitive reactance is exploited in coupling capacitors (blocking DC while passing AC), bypass/decoupling capacitors (providing a low-impedance path to ground for AC noise), filter networks (with the Resonant Frequency Calculator determining the crossover point), power factor correction (cancelling inductive reactance from motors), and timing circuits (where the RC time constant depends on reactance at a specific frequency).
Frequently Asked Questions
Does a capacitor have resistance?
What happens at DC?
Why use a bigger capacitor for lower frequencies?
What is the self-resonant frequency of a capacitor?
Can I use this calculator for impedance matching?
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