Reactance and Impedance

Impedance meaning – It is the measure of overall opposition of a circuit to current denoted by Z. In simple words, it gives the amount of circuit that impedes the flow of change. Impedance is like resistance, which also takes into account the effects of inductance and capacitance. The measurement unit for Impedance is ohms.

As impedance considers the effects of inductance and capacitance and varies with the frequency of current passing through the circuit, it is more complex than resistance. As compared to resistance, which is constant regardless of frequency, impedance varies with frequency.

When it comes to define reactance, it is the measure of opposition of inductance and capacitance to current. Let’s learn more about these two terms in brief.

Impedance Formula

The mathematical symbol of impedance is Z, and the unit of measurement is ohm. It is the superset of both resistance and reactance combined.

In phasor terms, impedance Z is characterized as a summation of resistance R and reactance X as:

X = R + j X

Where reactance X is the summation of Inductive reactance XL and capacitive Xc

X = XL + Xc

Impedance, Z=V/I

Resistance, R= V/I

V = voltage in volts (V)

I = current in amps (A)

Z= impedance in ohms (Ω)

R= resistance in ohms (Ω)

Impedance can be splitted into two parts:

  • Resistance R (a part which is constant regardless of frequency)

  • Reactance X (a part which varies with frequency due to capacitance and inductance)

The alternating current lags or leads the voltage depends upon the nature of reactance component of impedance (whether predominantly inductive or capacitance)

The inductance and capacitance causes phase shift between current and voltage, which means the resistance and reactance cannot be simply summed up to give impedance. Instead, they must be summed up as vectors with reactance at right angles to resistance, as shown in the figure below.

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Impedance Z  = \[\sqrt{R^{2} + X^{2}}\] 

There are four electrical quantities which determine the impedance (Z) of a circuit: These are: resistance (R), capacitance (C), inductance (L) and frequency (f).

What Is Reactance?

The measure of opposition of inductance and capacitance to current is known as reactance, denoted by X. It varies with the frequency of electrical signals and is measured in ohms.

Reactance is of two types:

  • Capacitive reactance (Xc), and

  • Inductive reactance (XL).

Reactance formula

The total reactance (X) is equal to the difference between the two:

Total Reactance, X =XL – Xc

a. Capacitive Reactance Xc

The reactance, which is large at low frequencies and small at high frequencies is known as capacitive reactance (Xc). Xc is infinite for steady DC, at zero frequency (f=0Hz). This means that the capacitor passes AC but blocks DC.

Capacitive Reactance, Xc = 1/2fC

Where,

Xc=reactance in ohms (Ω)

f =frequency in hertz (Hz)

C =capacitance in farads (F)

For eg: 1µF capacitor has a reactance of 3.2k for 50Hz signal, but when a frequency is higher at 10kHz, the reactance is only 16.

b. Inductive Reactance, XL

The reactance which is small at low frequencies and large at high frequencies is known as inductive reactance. XL is zero for steady DC, at zero frequency (f=0Hz). This means that the inductor passes DC but blocks AC.

The formula for calculating inductive reactance of a coil is:

Inductive reactance, or XL, is a product of 2 times p (pi), or 6.28, frequency of the ac current in hertz, and the inductance of the coil, in henries.

XL =2p x f x L

L= the inductance value of coil in henries.

Inductive Reactance, XL=2fL

Where,

XL =reactance in ohms (Ω)

f    =frequency in hertz (Hz)

L   =inductance in henrys (H)

For example, a 1mH inductor has a reactance of only 0.3 for a 50Hz signal, but when frequency is higher at 10 kHz, its reactance is 63.

Do you know?

When current and voltage are out of step with each other, it means there is a phase shift. For example, when you change a capacitor, the voltage across it is zero. However the current is maximum. When the capacitor is charged, the voltage will be maximum, and current will be at minimum. The charging and discharging occur continually with AC, where the current reaches maximum shortly before the voltage reaches maximum, so it is called current leading voltage.

FAQ (Frequently Asked Questions)

1. How do you calculate reactance from impedance?

Ans- To calculate impedance, calculate resistance and reactance of a circuit, label resistance as R and reactance as X. Square both R and X, and sum the two products together. Take the square root of the sum of the squares of R and X to get impedance. Display the answer in ohms.

Impedance Z = V/I

Z = √R2 + X2

Z2= (R2+X2)


2. What is the difference between resistance, reactance, and impedance?

Ans- The measure of opposition to current flow offered by a material is known as resistance, denoted by R.

The resistance offered to ac currents only by inductors and capacitors is known as reactance, denoted by X.

For capacitor X=1/(2πfC), where f is frequency, and C is capacitance.

For inductor X= 2πfL, where f is frequency, L is inductance.

Impedance is the summation of resistance and reactance of circuit

Symbolized for primarily inductive circuit Z=R+jX or for primarily capacitive circuit Z=R-jX.

Where j=√(-1).

3. When should I use impedance instead of reactance vice versa?

Ans- There is a phase shift between voltage and current, and Impedance is sensitive to frequency.

Reluctance is a measure of resistance of an ideal coil at a specific frequency.

Reactance is a measure of resistance of an ideal capacitor at a specific frequency.

As an engineer:

Coils are imperfect, and the wire has an intrinsic resistance and loops form stay capacitance. Thus, a coil has resistance, reactance, and reluctance; this combination is a measure of its impedance.

Resistors are also imperfect, wire wound resistors have inductance to give small reluctance, and some surface mount resistors have tiny capacitance.

Normally speaking, if there is a dc circuit, you need to use resistance, and if the circuit is ac, you need impedance. 

4. What is the difference between reactance and resistance?

Ans- The opposition of the inductor to change the current is usually translated as the alternating current, which by definition, always varies in instantaneous size and direction.

This is similar to resistance, but different in that it always results in phase shift between current and voltage and it disperse zero power. Due to the difference, it has a different name reactance. Just like resistance, reactance to AC is measured in ohms, but its mathematical symbol is X instead of R.

Some more difference between Reactance and Resistance is:

Parameter

Resistance

Reactance

Variation in current

It is the property of the electrical component which opposes the flow of current.

It is the property of the electrical component which opposes the change in current.

Power Dissipation

It leads to power dissipation

It does not lead to power dissipation.

Denoted by

It is denoted by R

It is denoted by X