Reactance is the opposition that a capacitor or inductor presents to alternating current (AC) due to energy being stored and released in electric or magnetic fields. It is measured in ohms (Ω) and is frequency-dependent. Inductive reactance XL increases with frequency, while capacitive reactance XC decreases with frequency.

What is the formula for inductive reactance?

The formula for inductive reactance is XL = 2π f L, where XL is inductive reactance in ohms (Ω), f is frequency in hertz (Hz), and L is inductance in henries (H).

What is the formula for capacitive reactance?

The formula for capacitive reactance is XC = 1 / (2π f C), where XC is capacitive reactance in ohms (Ω), f is frequency in hertz (Hz), and C is capacitance in farads (F).

How do I calculate impedance from resistance and reactance?

For a simple series circuit, impedance magnitude is Z = √(R² + X²), where R is resistance and X is net reactance (positive for inductive, negative for capacitive). The phase angle is φ = arctan(X / R).

What happens at resonance in an RLC circuit?

In a series RLC circuit, resonance occurs when inductive and capacitive reactances are equal in magnitude (XL = XC). Net reactance becomes zero, so the impedance is purely resistive and equal to R. Current is maximized and the phase angle is zero.

Reactance Calculator: Inductive & Capacitive Reactance vs Frequency

Reactance basics

In AC circuits, reactance is the opposition that inductors and capacitors present to changing current. Unlike resistance, which dissipates energy as heat, reactance stores energy in magnetic (inductor) or electric (capacitor) fields and then returns it to the circuit.

Inductive reactance

\[ X_L = 2\pi f L \]

\(X_L\): inductive reactance (Ω)
\(f\): frequency (Hz)
\(L\): inductance (H)

Higher frequency or larger inductance → larger \(X_L\).

Capacitive reactance

\[ X_C = \frac{1}{2\pi f C} \]

\(X_C\): capacitive reactance (Ω)
\(f\): frequency (Hz)
\(C\): capacitance (F)

Higher frequency or larger capacitance → smaller \(X_C\).

Reactance and impedance

Reactance is the imaginary part of impedance \(Z\). For simple series circuits:

Pure resistor: \(Z = R\)
Pure inductor: \(Z = jX_L\)
Pure capacitor: \(Z = -jX_C\)
Series RLC: \(Z = R + j(X_L - X_C)\)

The impedance magnitude and phase angle are:

\[ |Z| = \sqrt{R^2 + X^2}, \quad \varphi = \tan^{-1}\left(\frac{X}{R}\right) \]

where \(X = X_L - X_C\) (positive for net inductive, negative for net capacitive).

Resonance in a series RLC circuit

At the resonant frequency, inductive and capacitive reactances cancel:

\[ X_L = X_C \quad \Rightarrow \quad 2\pi f_0 L = \frac{1}{2\pi f_0 C} \] \[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]

At resonance, net reactance is zero, so the impedance is purely resistive and equal to \(R\). Current is maximized and the phase angle is 0°.

Worked example: inductive reactance

Suppose you have a 10 mH inductor at 50 Hz.

Convert units: \(L = 10 \text{ mH} = 10 \times 10^{-3} \text{ H} = 0.01 \text{ H}\).

\[ X_L = 2\pi f L = 2\pi \times 50 \times 0.01 \approx 3.14 \ \Omega \]

Worked example: capacitive reactance

A 10 µF capacitor at 50 Hz:

\(C = 10 \text{ µF} = 10 \times 10^{-6} \text{ F} = 10^{-5} \text{ F}\)

\[ X_C = \frac{1}{2\pi f C} = \frac{1}{2\pi \times 50 \times 10^{-5}} \approx 318.3 \ \Omega \]

FAQ

Is reactance the same as resistance?

No. Both are measured in ohms, but resistance dissipates power as heat, while reactance stores and releases energy in fields. In AC analysis, they combine into complex impedance \(Z = R + jX\).

Why does inductive reactance increase with frequency?

Inductors oppose changes in current. At higher frequencies, current changes more rapidly, so the inductor develops a larger voltage for the same current, appearing as a higher opposition (larger \(X_L\)).

Why does capacitive reactance decrease with frequency?

Capacitors oppose changes in voltage. At higher frequencies, the capacitor charges and discharges more often per second, allowing more current to flow for the same voltage amplitude, so \(X_C\) becomes smaller.