Impedance

Impedance is the total opposition a circuit offers to alternating current (AC); for DC, it is simply resistance. It is a vector quantity. It is denoted by Z and measured in ohms (Ω).

Definition

The magnitude of impedance is the amount of voltage applied across the circuit divided by the maximum amount of current passing through the circuit.

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Components of Impedance

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Relation Between Impedance, Inductive and Capacitive Reactance

The resistance component is indicated by a vector along the horizontal (x) axis, and the inductive reactance by a vector along the vertical (y) axis. The total impedance is indicated by a vector originating at the start and moving to a point that adds both the resistance (in the x-direction) and the inductive reactance (in the y-direction). To find the electrical impedance in a circuit that contains both resistance and inductive reactance, use the following formula. If capacitive reactance is present in the circuit, its value is added to the reactance before squaring.

Formula -

|Z| = √(R² + X²)

The impedance can also be represented as a complex number with the resistance as the real part and the reactance as the imaginary part.

Z = R + iX

where,

Base = Resistance (R)

Perpendicular = Reactance (X)

Hypotenuse = Impedance (Z)

Impedance triangle showing Resistance R, Reactance X and Impedance Z

Phase Angle

The phase angle θ between the voltage and current is given by:

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If X_c > X_L, then θ it is negative, and the circuit is capacitive. The current in the circuit leads the source voltage.
If X_c < X_L, then θ it is positive, and the circuit is inductive. The current in the circuit lags the source voltage.

Impedance in Different Forms

Component	Impedance (Z)
Resistor	Z = R
Inductor	Z = jωL
Capacitor

Applications of Impedance

Electrical Engineering: Impedance is utilised in electronic, communication, and power system circuit design.
Audio Systems: Amplifier and speaker impedance matching will improve sound quality.
Medical Equipment: Impedance is used by devices such as ECGs and EEGs to identify signals.
Power Transmission: Impedance influences the flow of electricity in long-distance transmission lines.
Signal Processing: Impedance is a major contributor to filters, oscillators, and radio-frequency circuits.

Summary

Impedance is the sum of opposition provided by an electric circuit to AC. It's the combination of resistance (R), which is against both AC and DC and reactance (X), which is only against AC and is a function of frequency. Impedance is expressed as a complex number Z = R + jX and is measured in ohms (Ω). Resistance is on the x-axis, and reactance on the y-axis, with impedance as the diagonal vector from the origin. The impedance is expressed as |Z| = √(R² + X²) and the phase angle determines whether or not the current is ahead of or behind the voltage, depending on the reactance type.

Frequently Asked Questions

Q1. State the difference between resistance and impedance

Resistance opposes both AC and DC and stays constant, while impedance applies only to AC and includes both resistance and frequency-dependent reactance.

Q2. What is reactance?

Reactance is the opposition caused by inductors or capacitors in an AC circuit. It depends on the frequency of the current.

Q3. Why is impedance important in AC circuits?

Impedance helps determine the amount of current that will flow, and it also affects circuit behaviour.