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Can you help me to check if the results of the following circuit are right?

The exercise asks: find the \$V_{3}(t)\$ and \$I_{3}(t)\$ having \$V_{2}(t)= \cos(2t + 165^\circ)\$ and \$I_{5}(t)=2\sin(2t -30^\circ)\$

My results are: \$I_{3}(t) = 0.3425\cos(2t + 162^\circ)\$ \$V_{3}(t) = 1.0274\cos(2t + 162^\circ)\$

enter image description here

The voltage source on the left is \$V_{2}(t)\$

Here is my attempt:

Mesh method:

enter image description here

$$\left[\begin{matrix} 1-\frac{3}{4}J&\frac{J}{2} \\\\ \frac{J}{2}&3-\frac{J}{2} \\\\ \end{matrix}\right] \left[\begin{matrix} I_1 \\\\ I_2 \\\\ \end{matrix}\right] = \left[\begin{matrix} -0.433+0.25J \\\\ -0.966+0.2588J \\\\ \end{matrix}\right]$$

This solves to:

$$I_{1}=-0.44157+0.0818J$$

$$I_{2}=-0.326+0.1055J$$

So \$I_{3}(t) = 0.3425\cos(2t + 162^\circ)\$ and \$V_{3}(t) = 1.0274\cos(2t + 162^\circ)\$

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    \$\begingroup\$ Why not use a circuit simulator to check your result? They can be obscenely accurate for circuits like this. They are also free. \$\endgroup\$
    – Andy aka
    Feb 24, 2023 at 11:06
  • \$\begingroup\$ Can you link the site? \$\endgroup\$ Feb 24, 2023 at 11:13
  • \$\begingroup\$ I use micro-cap download link: spectrum-soft.com/download/mc12cd.zip \$\endgroup\$
    – Andy aka
    Feb 24, 2023 at 11:17
  • \$\begingroup\$ I'm having trouble to measure the current and the voltage with the software can you do it for me? \$\endgroup\$ Feb 24, 2023 at 12:25
  • \$\begingroup\$ My recommendation is that you try and resolve the sim software yourself. But, you could also post the sim schematic into your question as a formal edit. Micro-cap (like LTspice) is a very powerful tool and, I encourage anyone thinking of EE as a job to learn it. I use it for everything because it catches problems and double checks my thinking. \$\endgroup\$
    – Andy aka
    Feb 24, 2023 at 12:33

1 Answer 1

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The results are the following:

\$V_3(t) = 1.028 \cos(2t + 162°)\$

\$I_3(t) = 0.343 \cos(2t + 162°)\$

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