What is Impedance? Explained

Impedance is the total opposition a cable or circuit offers to alternating current (AC). It includes both resistance and reactance and is measured in ohms (Ω). Impedance determines how easily AC signals move through a circuit, affecting voltage, current, and power. To understand how impedance interacts with voltage, explore our explanation of what is voltage and how it affects current flow in electrical circuits.

What is Impedance?

✅ Combines resistance and reactance in AC circuits

✅ Measured in ohms and affects signal flow and power

✅ Essential in analyzing voltage, current, and circuit behavior

Impedance Formula and Complex Representation

Impedance is defined mathematically by the formula:

Z = V / I

Where:

• Z is impedance in ohms (Ω)

• V is voltage (volts)

• I is current (amperes)

In AC systems, impedance is expressed as a complex impedance:

Z = R + jX

Where:

• R is resistance (real part)

• X is reactance (imaginary part)

• j is the imaginary unit

This complex form accounts for both magnitude and phase angle, which are essential in understanding how voltage and current interact in AC circuits.

Frequency, Phase Angle, and Reactance

Impedance depends on frequency. As frequency increases, reactance (especially inductive and capacitive) also changes, which shifts the phase angle between voltage and current.

• Inductive reactance (XL = 2πfL) increases with frequency

• Capacitive reactance (XC = 1 / 2πfC) decreases with frequency

This means that the total impedance of a circuit can vary significantly depending on the frequency of the signal. Engineers must account for this when analyzing harmonics or designing high-frequency systems. Learn how resistance contributes to impedance by reviewing what is electrical resistance and how it differs from reactance in AC systems.

Common Applications of Impedance

Understanding impedance is critical in many areas of electrical and electronic engineering:

• Audio Systems: Proper impedance matching ensures maximum power transfer and sound clarity between amplifiers and speakers.

• Radio Frequency (RF): Antenna design and transmission lines rely on precise impedance matching to minimize signal loss.

• RLC Circuits: Impedance analysis allows for tuning and resonance calculations in resistor-inductor-capacitor networks.

• Power Systems: Impedance affects fault current calculations, load flow, and harmonic analysis.

• Phasor Analysis: Engineers use phasors to represent voltage and current in the frequency domain, relying on impedance to model AC behavior. For insights into the capacitive elements of impedance, see what is a capacitor and how it stores energy in electric fields.

Power System Impedance (Advanced)

At the fundamental frequency, power systems are primarily inductive, and the equivalent impedance is often referred to simply as the short-circuit reactance. Capacitive effects are often overlooked in utility distribution systems and industrial power systems. One of the most frequently used quantities in the analysis of harmonics on power systems is the short-circuit impedance to the point on a network at which a capacitor is located. If not directly available, it can be computed from short-circuit study results that give either the short-circuit WA or the short-circuit current as follows:

However, if the short-circuit data contains no phase information, one is usually constrained to assuming that the impedance is purely reactive. This is a reasonable assumption for industrial power systems, for buses near the mains, and for most utility systems. When this is not the case, an effort should be made to determine a more realistic resistance value, as it will affect the results once capacitors are taken into account. Discover how impedance plays a role in AC power systems by reading about what the power factor is and how it affects energy efficiency.

The inductive reactance portion of the impedance changes linearly with frequency. One common error made by novices in harmonic analysis is forgetting to adjust the reactance for frequency. The reactance at the h-th harmonic is determined from the fundamental impedance reactance, X1, by

 In most power systems, one can generally assume that the resistance does not change significantly when studying the effects of harmonics less than the ninth. For lines and cables, the resistance varies approximately as the square root of the frequency once the skin effect becomes significant in the conductor at higher frequencies.

The exception to this rule applies to certain transformers. Due to stray eddy current losses, the apparent resistance of larger transformers may vary almost in proportion to the frequency. This can have a highly beneficial effect on damping resonance, as shown later. In smaller transformers, less than 100 kVA, the resistance of the winding is often so large relative to the other impedances that it swamps out the stray eddy current effects, and there is little change in the total apparent resistance until the frequency reaches about 500 Hz. Of course, these smaller transformers may have an XIR ratio of 1.0 to 2.0 at fundamental frequency, while large substation transformers might typically be 20 to 30.

Therefore, if the bus that is being studied is dominated by transformer impedance rather than line impedance, the system impedance model should be considered more carefully. Neglecting the resistance will generally give a conservatively high prediction of the harmonic distortion. Impedance matching is especially important in signal transmission—see how it's influenced by alternating current and ohm’s law in real-world applications.

At utilization voltages, such as those in industrial power systems, the equivalent system reactance is often dominated by the service transformer's impedance. A good approximation for Xc may be based on the impedance of the service entrance transformer only:

While not precise, this is generally at least 90% of the total impedance and is commonly more. This is usually sufficient to determine whether there will be a significant harmonic resonance problem. Transformer impedance in ohms can be determined from the percent impedance, Z, found on the nameplate by:

Z (Ω) = (Z% / 100) × (V² / kVA)

where MVA is the kVA rating of the transformer, this assumption is based on the fact that the impedance is predominantly reactive. For example, for a 1500 kVA, 6% transformer, the equivalent impedance on the 480 V side is

Z = (6 / 100) × (480² / 1500) = 9.22 ohms (example approximation)

Impedance is a fundamental concept in AC circuit analysis, combining resistance and reactance to determine how electrical energy flows through systems. Expressed as a complex value, impedance varies with frequency and plays a critical role in everything from audio engineering and RF systems to industrial power distribution and transformer behaviour. Understanding how impedance affects phase angle, signal flow, and power quality is essential for engineers and technicians designing or analyzing electrical systems. Whether you're matching components in a speaker system or modelling harmonic resonance in a utility network, mastering impedance is key to optimizing performance, efficiency, and safety.

Related Articles

• Electricity Fundamentals

• Electricity Questions

• Electricity History

•