Reactance is a fundamental concept in electronics. Here’s what reactance is and how it manifests itself, and the formulas needed to calculate it easily.
The inductive reactance of an inductor depends on its inductance and the applied frequency. This reactance increases linearly with increasing frequency. This relationship can be expressed by a formula to calculate the reactance at a specific frequency.
During our studies, we often find ourselves dealing with rather complex topics. Among these, those related to electronics can present several difficulties.
One of the most difficult topics in this field is reactance. In this short guide, we will explore the steps needed to calculate reactance in a simple and clear way.
Increase in frequency
Let’s start by saying that reactance is a fundamental component of impedance , studied in the field of electronics in alternating current electrical circuits . It is commonly represented by the letter X and is measured in ohms , the same unit of measurement as impedance.
Reactance creates a phase discrepancy between the circuit voltage and the current flowing through it. In a purely capacitive or inductive circuit, the impedance consists solely of capacitive or inductive reactance .
The reactance of an inductor or capacitor is calculated by the algebraic sum of their individual reactances. From the equation of inductive reactance, it can be noted that by increasing the frequency or inductance, the overall value of the inductive reactance also increases.
As the frequency approaches infinity, the reactance of the inductors increases without limit, behaving as an open circuit. On the contrary, as the frequency approaches zero (direct current, DC), the reactance of the inductors drops to zero, acting as a short circuit.
In summary, inductive reactance is “proportional” to frequency: it increases with frequency, being low at low frequencies and high at high frequencies. Therefore, at DC, an inductor has zero reactance (short circuit), while at high frequencies it has infinite reactance (open circuit).
Constitutive report
The reactance of an inductor represents the resistance, expressed in ohms, at the operating frequency. Knowing its value is essential for the calibration of attenuators, couplers and filters of various types. The constitutive relation of inductors is expressed by the formula v = L ⋅ di/dt , where “L” is the inductance of the inductor.
Considering the derivation property of phasors, we obtain the formula V = jωLI , where “V” is the voltage phasor and “I” is the current phasor. From this relationship, we can derive the impedance, defined as the ratio of the current phasor to the voltage phasor, which is Z = jωL . Then, the formula for inductive reactance, i.e., the reactance of the inductor, is X = ωL .
Reactance value
The reactance of a capacitor, when an alternating current passes through it, is called capacitive reactance. It is measured in ohms, just like inductive reactance, and represents the resistance opposed by the capacitor at the operating frequency. Knowing the value of capacitive reactance is essential for the calibration of attenuators, various types of couplers and filters.
The constitutive relation of the capacitor is expressed by the formula: i = C ⋅ dv/dt , where “C” represents the capacitance of the capacitor. Considering the derivation of the phasors, we obtain: I = jωCV .
From this relation we can obtain the impedance of the capacitor, defined as: Z = V/I = 1/jωC = j/ωC .
The impedance, which has only an imaginary part, allows us to obtain the capacitive reactance with the following formula: X = -1/ωC .
