Electrical impedance

Electrical Impedance

Electrical impedance is a fundamental concept in the field of electrical engineering and physics, particularly relevant in the study of alternating current (AC) circuits. It is a measure of the opposition that a circuit presents to the passage of a current when a voltage is applied. Impedance extends the concept of resistance to AC circuits and is a complex quantity, encompassing both magnitude and phase.

Definition

In mathematical terms, electrical impedance \( Z \) is defined as the ratio of the complex voltage \( V \) across an element to the complex current \( I \) through it:

\[ Z = \frac{V}{I} \]

Impedance is expressed in ohms (\( \Omega \)), similar to resistance, but unlike resistance, it is a complex number. It can be represented in the form:

\[ Z = R + jX \]

where: - \( R \) is the real part, known as the resistance. - \( X \) is the imaginary part, known as the reactance. - \( j \) is the imaginary unit, \( j^2 = -1 \).

Components of Impedance

Impedance consists of two components:

Resistance (R)

Resistance is the real part of impedance and represents the opposition to current flow in a circuit due to resistive elements. It is independent of frequency and is present in both AC and direct current (DC) circuits.

Reactance (X)

Reactance is the imaginary part of impedance and arises from the presence of capacitors and inductors in a circuit. Reactance varies with frequency and can be further divided into:

• Capacitive Reactance (\( X_C \)): Occurs in circuits with capacitors and is inversely proportional to the frequency of the AC signal.

 \[
 X_C = \frac{1}{2\pi fC}
 \]
 where \( f \) is the frequency and \( C \) is the capacitance.

• Inductive Reactance (\( X_L \)): Occurs in circuits with inductors and is directly proportional to the frequency of the AC signal.

 \[
 X_L = 2\pi fL
 \]
 where \( L \) is the inductance.

Phasor Representation

In AC analysis, impedance is often represented using phasors, which are complex numbers that represent the magnitude and phase of sinusoidal functions. The phasor form of impedance is useful for simplifying the analysis of AC circuits.

Impedance in AC Circuits

In AC circuits, impedance plays a crucial role in determining the current flow and voltage distribution. The total impedance in a series circuit is the sum of the individual impedances, while in a parallel circuit, the total impedance is given by the reciprocal of the sum of the reciprocals of the individual impedances.

Applications

Electrical impedance is used in various applications, including:

• Impedance Matching: Ensuring that the impedance of a source and load are matched to maximize power transfer and minimize reflections in transmission lines.
• Medical Impedance Tomography: A technique used in medical imaging to reconstruct the internal conductivity of a body from surface electrical measurements.
• Audio Engineering: Impedance is crucial in the design of audio equipment to ensure compatibility between different components.

Also see

• Resistance
• Reactance
• Alternating Current
• Phasor
• Impedance Matching