Circuit Theory/Phasors/Examples/example11

Complex 2R, L, C, voltage circuit

Given that the voltage source is defined by $V_{s}(t)=cos(t)$ and the current source is defined by $I_{s}(t)=2sin(t-{\frac {\pi }{3}})$ , find all other voltages, currents and check power.

Circuit marked up for analysis

Knowns, Unknowns and Equations

Knowns:

V_{s},R_{1},R_{2},L,C,I_{s}

Unknowns:

v_{1},v_{2},v_{C},v_{L},i_{1},i_{2},i_{C},i_{L}

Equations:

v_{1}=R_{1}*i_{1}

v_{2}=R_{2}*i_{2}

i_{C}=C*{d \over dt}v_{C}

v_{L}=L*{d \over dt}i_{L}

i_{1}+I_{s}-i_{2}-i_{C}=0

i_{c}-I_{s}-i_{L}=0

v_{1}+v_{2}-V_{s}=0

v_{C}+v_{L}-v_{2}=0

Solutions and Analysis

numeric solution calculated in the phasor domain

attempt at a Laplace solution

simulation at circuitlab

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.