Circuit Theory/Complex Frequency Examples/example15

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RC parallel, RL series circuit for example 15 circuit theory wikibook .. simple problem with complex frequency
solved with mupad code
put in phasor form with matlab m-file

Find everything give that:

V_s = 10 * e^{-100t} \cos(6000t)

Terminal Relations:

\mathbb{V}_2 = R_1 * \mathbb{I}_2
\mathbb{I}_3 = C_1 * s * \mathbb{V}_3
\mathbb{V}_1 = L_1 * s * \mathbb{I}_1
\mathbb{V}_4 = R_2 * \mathbb{I}_1

Junction Equation:

\mathbb{I}_1 - \mathbb{I}_2 - \mathbb{I}_3 = 0

Loop Equations:

\mathbb{V}_3 + \mathbb{V}_1 + \mathbb{V}_4 - \mathbb{V}_s = 0
\mathbb{V}_3 - \mathbb{V}_2 = 0 (trivial loop)

Complex Frequency:

 s = -100 + 6000j

Complex frequency source:

 \mathbb{V}_s = 10

Solving in the complex frequency domain:

Symbol Magnitude Radians Degrees
v1 13.8329 0.0455 2.6061
v2 3.8425 -3.0978 -177.4894
v3 3.8425 -3.0978 -177.4894
v4 0.4611 -1.5270 -87.4894
i1 0.2305 -1.5270 -87.4894
i2 3.8425e-04 -3.0978 -177.4894
i3 0.2305 -1.5253 -87.3939