WOLFRAM SYSTEM MODELER

ACCircuit

AC circuit

Wolfram Language

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SystemModel["Modelica.Electrical.QuasiStatic.UsersGuide.Overview.ACCircuit"]
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Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

A simple example of a series connection of a resistor, an inductor and a capacitor as depicted in Fig. 1 should be explained in the following. For various frequencies, the voltage drops across the resistor, the inductor and the capacitor should be determined.

resonance_circuit.png
Fig. 1: Series AC circuit of a resistor and an inductor at variable frequency

The voltage drop across the resistor


\underline{v}_{r}=R\underline{i}

and the inductor


\underline{v}_{l}=j\omega L\underline{i}

and the capacitor


\underline{v}_{l}=j\omega L\underline{i}

add up to the total voltage


\underline{v}=\underline{v}_{r}+\underline{v}_{l}

as illustrated in the phasor diagram of Fig. 2.

phasor_diagram.png
Fig. 2: Phasor diagram of a resistor and inductance series connection

Due to the series connection of the resistor, inductor and capacitor, the three currents are all equal:

img5.png

See also

Introduction, Power, Reference system