# AC steady state circuit analysis using mesh

I have attempted multiple tries into this circuit problem and I am getting no where. For this question I have to use mesh analysis to find $V_x$. $V_x$ is across the right branch containing the 3 ohm resistor and $-2j$ ohm capacitor. Everything is in impedances.

simulate this circuit – Schematic created using CircuitLab

After I setup my three loop equations, I got three unknowns, which seemed right because I setup three equations, but after substitution, I realise the final equation had two unknowns in it. However, I noticed since the straight branch of wire the $4j$ inductor and 10 volt source are in is in parallel with the right most branch containing the 3 ohm resistor and $-2j$ inductor, then both branches should have the same voltage. So that's what I did and set up another equation,

$$I_3(3-2j)=(I_3-I_1)(4j)+10$$

So when I tried to find $V_x$, where $V_x = (I_3)(3-2j)$, I get a value of 10, which is not correct because the answer is $V_x = 17.4(-21.625^{\circ})$ in phasors.

• If you use matrix methods, you have a straight path to the answer. However you need to learn it, but it isn't that much of a difference. For example nodal analysis Commented Sep 8, 2015 at 9:01