# Find the voltage and the current of the circuit

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)\$$

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

Here is my attempt:

Mesh method:

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

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)\$$

• Why not use a circuit simulator to check your result? They can be obscenely accurate for circuits like this. They are also free. Feb 24, 2023 at 11:06
• Can you link the site? Feb 24, 2023 at 11:13
$$\V_3(t) = 1.028 \cos(2t + 162°)\$$
$$\I_3(t) = 0.343 \cos(2t + 162°)\$$