Electrical impedance
Opposition to alternating current combining resistance and reactance.
Electrical impedance is a fundamental concept in electrical engineering that extends the idea of resistance to alternating current (AC) circuits. It quantifies the opposition to AC presented by the combined effect of resistance and reactance, possessing both magnitude and phase. Unlike resistance, which has only magnitude, impedance is represented as a complex number, with the same SI unit as resistance: the ohm. Its symbol is typically Z. The magnitude of impedance describes the ratio of the voltage amplitude to the current amplitude, while its phase indicates the phase difference between the voltage and current. Impedance can be expressed in polar form, showing magnitude and phase, or in Cartesian form, where the real part is resistance (R) and the imaginary part is reactance (X). The Cartesian form is convenient for adding or subtracting impedances, while the polar form simplifies multiplication and division. The reciprocal of impedance is admittance, measured in siemens. Instruments that measure electrical impedance are called impedance analyzers.
The concept of impedance is essential for AC circuit analysis, as it allows sinusoidal voltages and currents to be related by a linear law analogous to Ohm's law. In circuits with multiple ports, the two-terminal definition is insufficient, but voltages and currents at the ports are linearly related by an impedance matrix. The historical development of impedance began with Johann Victor Wietlisbach in 1879, who used complex numbers to analyze the Maxwell bridge, expressing AC currents and voltages as exponential functions with imaginary exponents. He found that voltage could be obtained by multiplying current by a complex number, though he did not recognize this as a general parameter. The term "impedance" was coined by Oliver Heaviside in July 1886, who identified the "resistance operator" in his operational calculus as a complex number. In 1887, Heaviside demonstrated an AC equivalent to Ohm's law. Arthur Kennelly published an influential paper in 1893, arriving at a complex number representation by building on John Ambrose Fleming's 1889 graphical method, which showed resistance, reactance, and impedance as sides of a right triangle. Kennelly realized this graphical representation was analogous to an Argand diagram, allowing algebraic treatment of impedances. Later that year, Charles Proteus Steinmetz gener
- field
- Electrical engineering
- symbol
- Z
- unit
- ohm (Ω)
- reciprocal
- admittance (siemens)
- components
- resistance (R) and reactance (X)
- forms
- polar form |Z|∠θ and Cartesian form R + jX
Lore & Background
Electrical impedance is a complex quantity that characterizes the opposition a circuit presents to alternating current, extending the concept of resistance to AC systems. Unlike resistance, which has only magnitude, impedance possesses both magnitude and phase. It is defined as the ratio of the complex representation of sinusoidal voltage across a two-terminal element to the complex representation of the current flowing through it, and this ratio generally depends on the frequency of the applied voltage. Impedance can be expressed in polar form, capturing its magnitude and phase angle, or in Cartesian form, where the real part is resistance and the imaginary part is reactance. Reactance arises from the effects of inductance (magnetic field induction) and capacitance (electrostatic charge storage). The SI unit for impedance is the ohm, the same as for resistance. Its reciprocal is admittance, measured in siemens. Instruments designed to measure this property are known as impedance analyzers. The concept originated with Johann Victor Wietlisbach in 1879, who used complex exponential functions to analyze a bridge circuit, effectively multiplying current by a complex number to find voltage. Oliver Heaviside coined the term "impedance" in 1886 and later showed an AC equivalent to Ohm's law. Arthur Kennelly, building on John Ambrose Fleming's graphical triangle representation, recognized that impedance could be added vectorially and corresponded to complex numbers on an Argand diagram, enabling algebraic calculations. Charles Proteus Steinmetz then generalized this approach to all AC circuits by representing voltages and currents as complex numbers, allowing direct AC equivalents of DC laws like Ohm's and Kirchhoff's laws. For multi-port networks, the two-terminal definition is insufficient, but voltages and currents remain linearly related through an impedance matrix.
Reader's Guide
Electrical impedance is central to AC circuit analysis, enabling the relationship between sinusoidal voltages and currents through a simple linear law. Its representation as a complex number—either in polar form (|Z|∠θ) or Cartesian form (R + jX)—allows engineers to handle both magnitude and phase. The real part is resistance, and the imaginary part is reactance, which arises from inductance and capacitance. Impedance extends the concept of resistance to AC circuits and is measured in ohms. Its reciprocal is admittance, measured in siemens. Instruments called impedance analyzers measure electrical impedance. The historical development by Heaviside, Kennelly, and Steinmetz established the complex representation that remains standard in electrical engineering. For multi-port networks, impedance is generalized into an impedance matrix. The concept is essential for network analysis, filter design, and transmission line theory.
Frequently Asked Questions
Who is Electrical impedance?
Electrical impedance is the AC-circuit counterpart to simple resistance, representing the total opposition a circuit element presents to alternating current. It is a complex quantity that captures both how much current is opposed and by what phase shift.
What are Electrical impedance's powers/role?
Its role is to fold pure resistance (R) and reactance (X) into a single value that fully describes how a component blocks AC flow. It can be written in Cartesian form as R + jX or in polar form as |Z|∠θ, letting engineers see both magnitude and phase at a glance.
What symbol and unit does Electrical impedance go by?
It is universally denoted by the letter Z and measured in ohms (Ω). Its reciprocal, admittance, is expressed in siemens and tells you how readily a circuit lets AC pass instead.
Why is Electrical impedance important to the Electromagnetism 1-21 cast?
Without impedance, engineers could not properly analyze AC circuits containing inductors and capacitors, since resistance alone ignores the energy-storage and phase-shift effects those components introduce. It is the key quantity that makes AC circuit analysis as tractable as its DC counterpart.
How does Electrical impedance's story end?
Its narrative arc resolves into admittance (Y = 1/Z), the reciprocal that flips the perspective from opposition to conductance. In practice the two are used interchangeably depending on whether a network is easier to model as a series or a parallel arrangement.
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