Apparent impedance

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

The apparent impedance (German: Scheinwiderstand, also Impedanz or (komplexer) Wechselstromwiderstand) is also referred to as (complex) impedance.

The impedance is a measure of the opposition that an electric circuit presents to an electric current, particularly with alternating current. Unlike the ohmic resistance, which is only relevant for direct current, the impedance plays an important role in the analysis of AC circuits. It does not appear in DC circuits in this script, because the ohmic resistance is used instead.

Central quantity in EE2

The impedance is the central quantity of AC circuit analysis (EE2). It is introduced in EE2-04 (Components in the AC circuit) and runs through all further EE2 lessons as a key concept. The mathematical foundation is provided by complex arithmetic (EE2-03).

Impedance of the basic components:

Component	Impedance	Phase angle
Resistor	${\underline{Z}}_R=R$	$\phi =0°$
Capacitor	${\underline{Z}}_C=\frac{1}{j\omega C}$	$\phi =-90°$
Inductor	${\underline{Z}}_L=j\omega L$	$\phi =+90°$

1 Quantity symbol and unit

The quantity symbol of the apparent impedance is $Z$.
It is a complex scalar quantity that comprises both the ohmic resistance and the Reactance (reactance of inductance and capacitance) of an electric circuit:

$$Z=R+jX$$

where:

• $R$ is the ohmic resistance, which forms the real part of the complex number
• $jX$ is the imaginary part of the complex number, where:
  • $j$ is the imaginary unit ($j=\sqrt{-1}$)
  • $X$ is the capacitive or inductive reactance
    The unit of the apparent impedance is the ohm, with the Greek capital letter omega ($\Omega$) as its unit symbol.

$$[Z]=\Omega$$

2 Practical and worked examples

2.1 Loudspeaker

‘The loudspeaker has an impedance of $4\mathrm{\Omega }$.’

$$|\underline{Z}|=4\mathrm{\Omega }$$

2.2 Complex AC circuit

‘The impedance of the AC circuit is approximately $42\mathrm{\Omega }$. It is made up of the ohmic resistance of $20\mathrm{\Omega }$ and an inductive reactance of $37\mathrm{\Omega }$.’

$$Z=20\mathrm{\Omega }+j37\mathrm{\Omega }=\sqrt{20^2+37^2}\mathrm{\Omega }=\sqrt{400+1369}\mathrm{\Omega }=\sqrt{1769}\mathrm{\Omega }=42.07\mathrm{\Omega }\approx \underline{42\mathrm{\Omega }}$$

with $R=20\mathrm{\Omega }$ in the real part and $X=X_L=37\mathrm{\Omega }$ in the imaginary part.

3 Typical orders of magnitude

• Headphones and loudspeakers: $4\mathrm{\Omega }$, $8\mathrm{\Omega }$, $16\mathrm{\Omega }$
• Microphones: $200\mathrm{\Omega }$ to $10\mathrm{k\Omega }$
• Coaxial cables: $50\mathrm{\Omega }$, $75\mathrm{\Omega }$
• RF circuits: $50\mathrm{\Omega }$ (standard impedance)
• Power supplies and filters: $1\mathrm{\Omega }$ to $100\mathrm{k\Omega }$
• Antenna inputs: $75\mathrm{\Omega }$ (TV), $50\mathrm{\Omega }$ (radio)

4 Example phrasings

• ‘The input impedance of the amplifier is $10\mathrm{k\Omega }$.’
• ‘For optimum power transfer, the impedance must be matched.’
• ‘The complex impedance has a magnitude of $50\mathrm{\Omega }$ and a phase angle of $30°$.’
• ‘At $1\mathrm{kHz}$, the capacitor exhibits a capacitive impedance of $159\mathrm{\Omega }$.’

5 Related quantities

• The impedance is made up of the ohmic resistance and the reactance.
• Together with the complex voltage and the complex current, the impedance appears in the complex form of Ohm’s law.
• Frequency ($f$): The reactance and thus the impedance are frequency-dependent
• Angular frequency ($\omega$): $X_L=\omega L$ and $X_C=\frac{1}{\omega C}$

6 Related components

• Inductor
• Capacitor
• Resistor
• Transformer