# AC circuit: Find the Va, Vb and the current through the 50 ohm resistor

#### michgkou

Joined Oct 3, 2019
41
Hi, I solve this using KCL, here is my try (hope there are no mistakes) :
* line 1: VD=V4

Now I want to solve it using KVL, my first attempt is below and I'm stuck. Any suggestions ?

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Thanks

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#### The Electrician

Joined Oct 9, 2007
2,866
For your KCL solution, when you get down the calculation of V1 by Cramer's method, you have a couple of incorrect values in the determinants:

On the next page where you calculate V3 you have the correct values, but you haven't evaluated the denominator determinant correctly.

You got 1051/5000 - j 89/625, but my calculator gets 195/5000 - j 369/5000

I think there may be at least one other minor error somewhere, but I haven't tracked it down yet.

I haven't checked the KVL solution yet either.

Edit: I just found the remaining error. You have a coefficient of 2/25 which should be 1/50:

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#### michgkou

Joined Oct 3, 2019
41
@The Electrician Thanks once again for your time and your answers.
Here is my try after the corrections:

#### The Electrician

Joined Oct 9, 2007
2,866
Everything looks ok with one exception. In your Cramer's rule calculation of V3, you have the wrong sign for the determinant of the numerator. You got it right in your first working, but then messed up the second try.

Are you doing all this complex arithmetic by hand? You've done enough of it by hand that you should consider graduating to using a calculator that can do complex arithmetic, or some appropriate app for your computer.

I'll look into the KVL solution later today.