Electrical Reactance: What is it? (Inductive & Capacitive)

Contents

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Key learnings:

Reactance Definition: Reactance is defined as the opposition to current flow in a circuit element due to inductance and capacitance.
Inductive Reactance: Inductive reactance, caused by inductors, stores energy in a magnetic field and makes current lag behind voltage.
Capacitive Reactance: Capacitive reactance, caused by capacitors, stores energy in an electric field and makes current lead voltage.
Reactance and Frequency: Inductive reactance increases with frequency, while capacitive reactance decreases with frequency.
Transmission Line Reactance: Transmission lines have both inductive and capacitive reactance, leading to phase differences and power losses.

What is Reactance?

Reactance (also known as electrical reactance) describes the frequency-dependent opposition to sinusoidal current caused by inductance or capacitance. It affects current magnitude and phase for an applied voltage. Reactance and electric resistance are both measured in ohms. Ideal reactance represents energy storage, while ideal resistance represents average energy dissipation.

In sinusoidal steady state, alternating current and voltage are represented as phasors. Reactance forms the imaginary term of the component impedance used to calculate their magnitude and phase relationship.

An ideal capacitor stores energy in an electric field, while an ideal inductor stores energy in a magnetic field. Each returns stored energy to the circuit during part of an AC cycle. An inductor opposes changes in current; a capacitor opposes changes in voltage.

Inductive reactance is positive under the usual impedance convention, while capacitive reactance is negative. Their magnitudes vary oppositely with frequency: inductive reactance increases as frequency rises, while capacitive reactance decreases.

An ideal resistor has zero reactance, whereas ideal inductors and capacitors have zero resistance.

Reactance Formula

Reactance is denoted by X. In a series circuit, total reactance is the algebraic sum of its signed terms. Inductive reactance (X_L) is positive and capacitive reactance (X_C) is negative. If the later capacitor formula is treated as a positive magnitude, subtract that magnitude from the inductive value.

$X = X_L + X_C$

For a purely inductive element, the capacitive term is zero:

$X = X_L$

For a purely capacitive element, the inductive term is zero. With signed reactance, this result is negative:

$X = X_C$

Like resistance and impedance, reactance is measured in ohms (Ω).

What is Inductive Reactance?

Inductive reactance is the reactance of an ideal inductor and is denoted by X_L. An inductor stores energy temporarily in its magnetic field.

A changing current through an inductor produces a changing magnetic flux linked with its winding.

The changing flux induces a voltage across the inductor. Under Lenz law, its polarity opposes the change in current that produced it.

This self-induced voltage is the basis of an inductor’s opposition to changing current.

For an ideal inductor driven by a sinusoidal source, current lags the voltage. This is a phase relationship, not a time delay applied to an unchanged waveform.

In a purely inductive circuit, current lags voltage by 90° and the power factor is zero lagging. Resistance in a real coil reduces the phase angle below 90°. The diagram shows the ideal case.

Phasor Diagram of Ideal Inductive Circuit

Inductive Reactance Formula

Inductive reactance is directly proportional to frequency for a constant ideal inductance.

For sinusoidal frequency f in hertz and inductance L in henries, its magnitude is:

$X_L = 2 \pi f L$

Unit of Inductive Reactance

Inductive reactance is measured in ohms (Ω).

What is Capacitive Reactance?

Capacitive reactance describes the frequency-dependent impedance of an ideal capacitor. Its magnitude is denoted by X_C; its signed reactance in Z = R + jX is negative.

A capacitor stores energy temporarily in the electric field between its conductors.

In a purely capacitive sinusoidal circuit, current leads voltage by 90° and the power factor is zero leading. Losses in a real capacitor reduce the phase angle below 90°. The diagram shows the ideal case.

Phasor Diagram of Ideal Capacitive Circuit

Capacitive Reactance Formula

The magnitude of capacitive reactance is inversely proportional to frequency f and capacitance C. Raising frequency reduces reactance; it does not reduce the capacitance value. The magnitude is:

$X_C = \frac{1}{2 \pi f C}$

Unit of Capacitive Reactance

Capacitive reactance is measured in ohms (Ω).

Reactance vs Impedance

Reactance X is the imaginary coefficient in impedance Z = R + jX. The quantities are related but not identical.

Reactance vs Resistance

The table compares reactance with Resistance under sinusoidal steady-state conditions.

Sr. No.	Reactance	Resistance
1	Reactance forms the imaginary term of impedance.	Resistance forms the real term of impedance.
2	Reactance is a signed real value multiplied by j in impedance.	Resistance is a non-negative real value for a passive component.
3	An ideal inductor or capacitor has no resistance.	An ideal resistor has no reactance.
4	Reactance produces a voltage-current phase difference.	Ideal resistance keeps sinusoidal voltage and current in phase and dissipates average power.
5	Ideal inductive and capacitive reactance depend on frequency.	Ideal resistance is constant, but real conductor resistance can vary with frequency.
6	At DC steady state, an ideal inductor is a short circuit and an ideal capacitor is an open circuit.	Ideal resistance follows the same V-I relation for DC and AC. Real values can vary with temperature and frequency.
7	It is denoted as X (X_L and X_C).	It is denoted as R.
8	Net reactance contributes to a leading or lagging power factor.	A purely resistive load has unity power factor.

Reactance of Transmission Line

In an electrical power system, a transmission line has distributed series inductance and shunt capacitance. Its model therefore includes both inductive and capacitive effects.

Line reactance affects voltage drop, phase angle and real-power transfer. Reactive power represents cyclic energy exchange between fields and the network; it is not itself an energy loss, although reactive current increases resistive losses in conductors.

Many power-system loads draw inductive reactive power. Shunt capacitors and other compensation equipment can supply reactive power locally, improve voltage and reduce current when correctly rated and controlled.

Operating power factor depends on the line, load and compensation. A lightly loaded long line can supply capacitive reactive power and may raise the receiving-end voltage, so its power factor is not necessarily close to unity.

Sr. No.	Reactance	Impedance
1	Series reactances combine as an algebraic sum of signed terms.	Series impedances combine as complex sums.
2	Reactance X is a signed real scalar in ohms.	Impedance Z is generally complex; a purely resistive impedance is real.
3	It is denoted as X.	It is denoted as Z.
4	$X = X_L + X_C$	$Z = R + jX$
5	Reactance is the coefficient of the imaginary impedance term in sinusoidal steady state.	Impedance is the phasor ratio of voltage to current at a stated frequency.
6	Reactance is zero for an ideal resistor.	An ideal resistor’s impedance is purely resistive.