Capacitive Reactance Calculator

Capacitive reactance is the opposition a capacitor presents to alternating current, measured in ohms and equal to 1/(2πfC). Unlike resistance it dissipates no power, because the current leads the voltage by 90° and energy flows into and back out of the electric field each cycle. A 100 µF capacitor at 50 Hz has a reactance of 31.83 Ω. Reactance is a magnitude only, so it must be combined with resistance vectorially rather than by simple addition.

Resonant frequency equals 1/(2π√(LC)). At that frequency the inductive and capacitive reactances are exactly equal and cancel, so a series circuit presents only its resistance and current reaches a maximum. With 10 mH and 100 µF the resonance sits at 159.155 Hz, where both reactances equal 10 Ω. Resonance is what makes radio tuning, induction heating and detuned harmonic filters work, and what makes untuned capacitor banks dangerous on harmonic-rich supplies.

The RC time constant, written τ, is R × C and gives the time in seconds for a capacitor to charge to 63.2 % of the applied voltage or to discharge to 36.8 % of its initial value. A 50 Ω resistor with a 100 µF capacitor gives 5 ms. Charging is treated as complete after five time constants, at 99.3 %, which is the figure used when sizing discharge resistors for safety and when estimating settling time in filters and timing circuits.

A capacitor opposes a change in the voltage across it, and it does so by moving charge. At a higher frequency the voltage reverses more often, so more charge must flow in and out each second, which means more current for the same applied voltage and therefore a lower effective opposition. Reactance is inversely proportional to frequency, so doubling the frequency halves the reactance. This is the opposite of an inductor, whose reactance rises with frequency, and it is why the two cancel at exactly one frequency.

The quality factor of a series RLC circuit equals (1/R)√(L/C). It measures how sharply the circuit selects its resonant frequency, and equals the resonant frequency divided by the bandwidth between the half-power points. A high Q above about 10 gives a narrow, sharp response suited to tuning, while a Q below 0.5 is overdamped and shows no real resonant peak at all. Resistance is what lowers Q, since it is the only element that dissipates energy.