Impedance and Complex Impedance

In Alternating Current, commonly known as the "AC circuit", impedance is the contrast of the current flowing around the circuit. Impedance is a value given in Ohm, the combined effect of current limiting components of circuits such as Resistance (R), Inductans (L) and Capacitance (C).

In a Direct Current or DC circuit, resistance to current flow is called, but in an AC circuit, impedance is the result of both the resistant (R) and reactive (X) components of the circuit. The amount of electrical resistance available in a DC circuit is indicated by the letter "R", while the letter "Z" or symbol for an alternative AC circuit is used to represent opposition to current flow.

Also, like DC resistance, impedance is expressed in Ohm and multiples and lower multiples of ohm value are used when appropriate.

For example, microhm (uΩ or 10-6), milliohm (mΩ or 10-3), kilohm (kΩ or 103) and megohms (MΩ or 106) etc. In any case, impedance can be defined using ohm law. NS:

Z = V/I, I = V/Z, V = I*Z

Where: Z is in Ohm, impedance is in V Volts and I amps.

Impedance Form

We have previously said that the total values of impedance (Z), resistance (R) and reacqueence (X) present in an AC circuit have a combined effect. But the impedance also depends on the frequency and therefore has a phase angle associated with it.

Whether inductive or capacitive, the phase angle of the reacquence is always out of phase 90o with the resistant component, so the resistant and reactive values of the circuits simply cannot be collected arithmetic to give the circuits the total impedance value. So R + X is not equal to Z.

It is worth noting here that the resistors do not change their values with frequency and therefore do not have recess (cable windings are not included), so their resistance is equal to their direct impedance (R = Z). As a result, the resistors do not have a phase angle, so the voltage and flowing current between them will always be "in-phase".

However, the reacktans in the form of inductive reacques, (XL) or capacitive reacques (XC) changes with frequency and causes the impedance value of the circuits to change as the feeding frequency changes. Therefore, ac circuit analysis sometimes uses the phrases "resistant impedance" (forresistors) and "reactive impedance" (for inductors and capacitors).

Since the resistant and reactive values of the circuits cannot be collected together to find the total impedance (Z), since the two values are 90o different from each other, that is, they are at a right angle to each other, so we can draw the values. A two-dimensional chart in which the x-axis is resistant or "real axis" and the y-axis is reactive or "imaginary axis". This is the same method used to make a right-angled triangle.

The right-angled graphics below show how resistance and reactance are combined to show the impedance with the hypotension (the longest edge) of the triangle, which represents the complex impedance of the circuit.

Resistance and Inductive Reactance

Impedance
Resistance and Inductive Reactance

When effectively dealing with what a three-edged right-angle triangle is, we can use pythagorean theorem and related equations to associate the two sides of the right-angled triangle, representing resistance and inductive rectangle, with the length of the third edge. hypotenuse. Pythagorean theorem is defined as follows in terms of impedance, resistance and reassurance:

Z^2 = R^2 + X^2

That is:

(Impedance)2 = (Resistance)2 + (Reactance)2

In this way we can show that the impedance vector (Z), resistance vector (R) and reactance vector (XL) are the resulting vector sum and have a positive slope as shown.

Impedance of an RL Circuit

Impedance
Impedance of an RL Circuit

Phase angle (φ) defines the angle in degrees between the impedance vector and the resistance vector, as shown below.

Phase Angle of an RL Circuit

Impedance
Phase Angle of an RL Circuit

As with the previous circuit, which includes an inductor and inductive reaccess, we can also show the complex impedance of an AC circuit containing capacitors and capacitive reaccess.

The same right-angle graph can be used to show how resistance and capacitive recess are combined with the hypotension (the longest edge) of the triangle, which represents the complex impedance of the circuit.

Note that for a capacitor, the impedance vector (Z), the resistance vector (R), and the reassurance vector (XC) are the vector sum. The negative slope is drawn in the opposite direction of the previous XL vector. This indicates that the effect of capacitive reactance on an AC circuit is the opposite of inductive reactance.

Resistance and Capacitive Reactance

Impedance

Again, using pythagorean theorems and equations, we can associate the two sides of the right-angle triangle, which represents resistance and capacitive recess, with the hypotenuse, which is a complex impedance. Pythagorean theorem is defined as follows in terms of impedance, resistance and reassurance:

Impedance of an RC Circuit

Impedance
Impedance of an RC Circuit

The tangent (φ) of the phase angle defines the angle between the impedance vector and the resistance vector in degrees. The phase angle is equal to the reassurance divided by resistance, as shown:

Phase Angle of an RC Circuit

Thus, vector diagrams can be used to show how resistance and reactance (inductive and capacitive) are combined to form impedance. We can also note that we can use the omic values of the circuit using Z, R or X to find the phase angle Φ between the supply voltage, VS and circuit current, I.

Impedance Sample Question

53mH inductor and 15Ω resistance are connected in series. Calculate total impedance and phase angle at 60Hz.

  1. Total Circuit Impedance, Z:
Impedance

2. Phase Angle, Φ:

Impedance

Impedance of an RLC Circuit

Reaction is Reaction! The impedance triangle of an inductor will have a positive slope, and the impedance triangle of a capacitor will have a negative slope, while the mathematical sum of the two impedances will produce the general impedance value of the circuits.

The combined coloract of the serial circuit will be the sum of XC of inductive reaccess, XL and capacitive reaccess, as shown.

X = XL + (-XC) = XL – XC

Impedance

As a general rule, whether it was XL or XC, we would subtract the smaller reassurance value from the larger value, it doesn't matter. This is because taking a square of a negative value always produces a positive result in mathematics. For example, -22 is the same result as +4 with 22.

Therefore, it is correct to use (XL – XC) or (XC – XL) to find the combined reaccount value of the circuits before adding them to the resistance value.

The resulting impedance triangle will look like this:

RLC Impedance Triangle

Impedance

The slope of the impedance is positive or negative in the direction, depending on which reactance is larger, with Inductive (XL – XC) or Capacitive (XC – XL). Then the circuit impedance in the complex form is defined as: Z = R ±jΕ

Clearly then, if an AC circuit contains only series of Inductans and Capacitance, impedance, Z = XL – XC or vice versa. If the circuit is in resonance, the net reacquency is zero, so the inductive reacquency is equal and opposite to capacitive reactance, so it is Z = 0 because XL = XC. Therefore, circuit current flow is limited to dynamic resistance (R) only in a series of resonance circuits.

Empedans Example

A non-inductive resistance of 10Ω, a capacitor of 100uF and an inductor of 0.15H are serially connected to a 240V, 50Hz source. Calculate inductive reactance, capacitive reactance, complex impedance of circuits and power factor.

Impedance

R = R = 10Ω

  1. Inductive Reactance, XL
Impedance

2. Capacitive Reactance, XC

Impedance

3. Complex Impedance, Z

Impedance

4. Power Factor

Impedance

In this article, we found that impedance, symbol Z, is the contrast of the current flowing around an AC circuit, and that resistance and reassurance have a combined effect. We also found that the impedance was not equal to the mathematical sum, but to the vector sum of the resistant and reactive components in the circuit,

The complex impedance in the series complies with the same Ohm Act rules as fully resistant circuits.

That is: ZT = Z1 + Z2 + Z3 + Z4 + … etc.

But what about the parallel connected circuits? How impedance is calculated for them.

Parallel Impedances

If a single resistance and a single recess are connected in parallel, each parallel branch must have impedance. But since there are only two components in parallel, R and X can use the standard equation for two resistances in parallel.

It is given as follows: RT = (R1*R2)/(R1 + R2).

Impedance

Where: Z, R, and X are all given in Ohm.

Also, when dealing with AC sources and frequencies, and therefore the resistant component is out of phase 90o with the reactive component, note that the product is divided by the sum of the R and X vectors.

Therefore, if the branches "n" containing complex impedances are connected to each other in parallel, the total impedance is the vector sum of all parallel branches. Thus, the opposite of the total impedance of the circuit is given as follows:

Impedance

And that's

Parallel Resistance and Inducing

Impedance

Parallel Resistance and Capacitance

Impedance

Resistance, Inductans and Capacitance in parallel

Impedance

Note here that for this RLC parallel circuit, at the resonance frequency, XL = XC is zero, so there is only resistance (R) in the circuit. Therefore, only in resonance, dynamic impedance is defined as: Z = R.