Loop analysis with complex components

[geft]

I'm supposed to find the currents flowing through the circuit. While loop analysis is pretty easy, converting a bunch of complex numbers back and forth can get complicated fast. I'm not asking for the exact answer, but please look through the solution to verify if my working is correct. Many thanks.

 

[gneill]

You might have a bit of a problem with the assumed directions of the loop currents versus the branch currents as defined when you write the loop equations. It shows up as an incorrect sign for your I3 value, yielding an incorrect angle.

I usually find it convenient to ignore the "ammeter" branch currents to begin with and solve for the mesh currents. Then go back and calculate the branch currents from them, taking into account their relative directions.

You also might consider carrying another decimal place or two through your intermediate results, as rounding errors are making their way into your first decimal place.

 

[geft]

Many thanks for the feedback. Assuming my calculation is correct, is I1 correct? Can't I3 be fixed by a simple sign change (after converting to rectangular form)?

 

[gneill]

Many thanks for the feedback. Assuming my calculation is correct, is I1 correct? Can't I3 be fixed by a simple sign change (after converting to rectangular form)?

The sign change will affect both components of the complex number, since the angle has to move from the 1st quadrant to the third quadrant.

 

[geft]

The sign change will affect both components of the complex number, since the angle has to move from the 1st quadrant to the third quadrant.

Why would it affect the magnitude (real component) if you can just add 180° to the phase?

 

[gneill]

Why would it affect the magnitude (real component) if you can just add 180° to the phase?

It affects the signs of the components.