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Just a brief hello before the problem! I am a new user as of today. I am studying Electrical Engineering in my spare time after work, and currently working full time an electronics service engineer. I have tried to make the problem as clear as I can, any help would be highly appreciated.

The problem asks to produce a current via two methods. I have obtained two answers that are different and would like to know where I went wrong.

For the record, most of my calculations were done within matlab. This is also my first attempt at using matrices, so I am unsure if my calculations were correct (or whether it was necessary to use matrices in the first place).

## Homework Statement

Determine the current I by

A) Mesh Analysis

B) Nodal Analysis

[tex]

\begin{align}

&v1 = 120 < 0° V\\

&v2 = 120 < 90° V\\

&v3 = 20 < 45° V\\

&z1 = 2 Ω\\

&z2 = –j5 Ω\\

&z3 = 4 Ω\\

&z4 = –j5 Ω\\

&z5 = j4 Ω\\

\\

&Node Voltages\\

&V10\\

&V20\\

&V30\\

&V40\\

\\

&Mesh Loops\\

&I1\\

&I2\\

&I3\\

&I4\\

\end{align}

[/tex]

## Homework Equations

## The Attempt at a Solution

A)[/B]

I1 -

[tex]v1-I1(z1+z4)+I2(z4) = 0[/tex]

[tex]I1(-2+j5)+I2(-j5) = -120[/tex]

I2 -

[tex]I1(z4)-I2(z2+z4+z5)+I3(z5)+I4(z2) = 0[/tex]

[tex]I1(-j5)+I2(j6)+I3(j4)+I4(-j5) = 0[/tex]

I3 -

[tex]I2(z5)-I3(z3+z5)-v2[/tex]

[tex]I2(j4)+I3(-4-j4) = j120[/tex]

I4 -

[tex]I2(z2)-I4(z2)-v3[/tex]

[tex]I2(-j5)+I4(j5) = 14.14+ j 14.14[/tex]

Matrix A

[tex]\begin{pmatrix}

-2+j5 & -j5 & 0 & 0\\

-j5 & j6 & j4 & -j5\\

0 & j4 & -4-j4 & 0\\

0 & -j5 & 0 & j5\\

\end{pmatrix}

[/tex]

Matrix B

[tex]\begin{pmatrix}

-120\\

0\\

j120\\

14.14+j14.14\\

\end{pmatrix}

[/tex]

[tex]

INV(A)*B = C

[/tex]

Matrix C - from matlab

[tex]\begin{pmatrix}

16.8112 - j22.8793\\

25.9629 - j40.1548\\

18.0588 - j22.0959\\

28.7914 - j42.9832\\

\end{pmatrix}

[/tex]

[tex]I = I1-I2-I4[/tex]

[tex]I = 16.8112 - j22.8793 - 25.9629 - j40.1548 - 28.7914 - j42.9832[/tex]

[tex]I = -37.9431 + j60.2587 A[/tex]

**B)**

[tex]V20 - V30 = V3[/tex]

**Node 2+3 supernode**

[tex]\frac{v1-V20}{z1} - \frac{V20}{z4} - \frac{V30}{z5} + \frac{v2-V30}{z3} = 0 [/tex]

[tex]X = V20(-0.5 - j0.5) + V30(-0.25+j0.25) = -60-j30 [/tex]

[tex] (V20-V30 = v3) * (-0.25+j0.25) [/tex]

[tex]Y = V20(-0.25+j0.25) + V30(0.25-j0.25) = -5\sqrt{2} [/tex]

**Add X + Y**

[tex]V20(-0.75+j0.05) = 67.07-j30[/tex]

[tex]V20 = \frac{-67.07-j30}{-0.75+j0.05}[/tex]

[tex]V20 = 86.37 + 45.76 V [/tex]

[tex]I = \frac{V20}{z4} = -9.15 +j17.27[/tex]

As you can see I have very different answers, and have scratched my head all weekend over it.

Any help would be appreciated.

Thanks!

Earthloop