Capacitive Reactance Calculator: X_c and RC Impedance

Capacitive reactance (Xc) is the opposition a capacitor presents to alternating current, measured in ohms (Ω). Unlike resistance, capacitive reactance does not dissipate energy as heat; instead, it stores and releases energy in an electric field. It is calculated as Xc = 1 / (2 * π * f * C), where f is frequency in hertz and C is capacitance in farads. A higher reactance means the capacitor impedes AC more strongly.

Capacitive reactance is inversely proportional to frequency. As frequency increases, Xc decreases, meaning the capacitor lets more current through. At very low frequencies approaching DC (0 Hz), Xc approaches infinity and no current flows. At very high frequencies, Xc approaches zero and the capacitor acts almost like a short circuit. This frequency-dependent behaviour makes capacitors useful in high-pass filters, coupling circuits, and decoupling power supplies.

In a purely capacitive circuit, current leads voltage by 90 degrees (the phase angle is -90 degrees). In an RC circuit, the phase angle is -arctan(Xc / R) and lies between 0 and -90 degrees depending on the ratio of reactance to resistance. A phase angle near 0 means the circuit is predominantly resistive; a phase angle near -90 degrees means the circuit is predominantly capacitive. The negative sign indicates the current leads the voltage.

Resistance (R) opposes current equally at all frequencies and converts electrical energy to heat. Capacitive reactance (Xc) opposes current in a frequency-dependent way without dissipating energy. In a phasor diagram, resistance lies along the real axis while capacitive reactance lies along the negative imaginary axis. Their combined effect is impedance (Z), which has both magnitude and phase. Resistance causes voltage and current to be in phase; capacitive reactance causes current to lead voltage.

Impedance (Z) in an RC series circuit is the total opposition to AC current from both resistance and capacitive reactance. It is calculated as Z = sqrt(R² + Xc²) and measured in ohms. Unlike reactance alone, impedance accounts for both the magnitude of the opposition and the phase relationship. The phase angle of the RC circuit is φ = -arctan(Xc / R). Impedance is used to calculate AC current using Ohm's law for AC: I = V / Z.