Circuit Mesh analysis question

[Toolkit]

Homework Statement

Homework Equations

I've worked out the KVL's for four meshes, I₁, I₂,I₃, and I₄. Would anyone be able to error check this for me?

Also, would I be correct in thinking that I can use ohm's law by dividing V₁/Z₁ to find the current of the first mesh and likewise with V₂/Z₃?

The Attempt at a Solution

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I₁ : I₁(-2Ω+J5Ω) -J5Ω(I₂) = 120∠0°v

I₂: -J5Ω(I₁) -J4Ω(I₂)+J4Ω(I₃)+J5Ω(I₄)=0

I₃: J4Ω(I₂) + J8Ω (I₃) = 120 ∠90°

I₄: J5Ω (-I₂) = J5Ω (I₄) = 20∠40°

Thanks,

Toolkit

 

[The Electrician]

Also, would I be correct in thinking that I can use ohm's law by dividing V₁/Z₁ to find the current of the first mesh and likewise with V₂/Z₃?

That would not be correct. The voltage across Z1 is not just V1. The voltage across Z4 is in series with V1 and those two voltages are then across Z1. The same reasoning applies to the voltage across Z3.

This problem requires close attention to signs of impedances and current directions. You should indicate on the schematic the mesh current directions you have assumed. A common convention is to assume mesh currents are clockwise as shown here. Node designations are also shown which will be handy when doing a nodal solution:

Have you tried solving your equations? I think you have some sign errors. I would write the mesh equations keeping the voltages and impedances in symbolic form (that is, use V2 instead of 120 /_90, use Z1 instead of 2 ohms, Z2 instead of -j5 ohms, etc.). Once you have them written out like that, double check the signs of voltages and currents. When you're sure you have all that right, substitute numerical values for the impedances and voltages.