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I have quite a problem regarding A.C. circuit analysis using complex numbers and 2x2 matricies. :yuck:

* The aim is to find the current in each of the two loops and apply Kirchoff's laws. I believe the overall aim is just to prove that the laws are actually in place..

(SEE ATTATCHMENT)

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Kirchoff's Law's:

1) The potential difference (voltage) in each loop must add up to zero

2) At any node (i.e. any circuit junction) the current flowing into the junction must equal the current flowing away from it.

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I've spent a long time looking at this but am finding it very confusing...

At first I thought it was a simple case of Ohm's law (for AC) to find the current ie. I = E / Z (aka I = V / R )

So I began looking for the current in the first loop (I1):

I1 = E1 / (Z1 + Z3) in the complex number form (using conjutives etc)

However this resulted in very obscure results and the j-operators (imaginary numbers) would not cancel out. I was hoping for a simple whole number.

SO now I'm back to square one. I'm sure I have to create a complex number formula, and then put these into a 2x2 matrix. But I don't know the necessary steps to take, or how exactly I would find the current.

I'm still not really sure on the purpose of Matricies either, could they be applied onto each circuit junction/node to evaluate currents going in and out and hence prove Kirchoff's laws? Or am I way off the mark.. is it more to do with phasors and sineforms?

Can anybody help? Thank you

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# Homework Help: Complex numbers, matricies and Kirchoff's laws

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