• Support PF! Buy your school textbooks, materials and every day products Here!

CIRCUITS: Current Controlled Voltage source, Indep. Voltage source, Four resistors

  • Thread starter VinnyCee
  • Start date
  • #1
489
0
Find [itex]v_1,\,v_2,\,and\,v_3[/itex] in the circuit below using nodal analysis:

PracticeProb3-4.jpg


My work so far:

[tex]I\,=\,\frac{v_1}{2\Omega},\,\,I_1\,=\,\frac{v_2}{4\Omega},\,\,I_2\,=\,\frac{v_3}{3\Omega},\,\,I_3\,=\,\frac{v_1\,-\,v_3}{6\Omega}[/tex]

KVL @ loop1 => [tex]-I\,(2\Omega)\,+\,10\,V\,+\,I_1(4\Omega)\,=\,0[/tex]

Which equals:
[tex]-\left(\frac{v_1}{2\Omega}\right)(2\Omega)\,+\,10\,V\,+\,\left(\frac{v_2}{4\Omega}\right)(4\Omega)\,=\,0[/tex]

Which equals:
[tex]-v_1\,+\,10\,V\,+\,v_2\,=\,0[/tex]

KVL @ loop2 => [tex]-v_2\,-\,5\,I\,+\,v_3\,=\,0[/tex]

KVL @ loop3 => [tex]-10\,V\,+\,v_1\,-\,v_3\,+\,5\,I\,=\,0[/tex]

KCL @ v1 => [tex]I\,+\,I_3\,+\,I_4\,=\,0[/tex]

KCL @ v2 => [tex]I_4\,=\,I_1\,+\,I_5[/tex]

KCL @ v3 => [tex]I_2\,=\,I_5\,+\,I_3[/tex]

KCL @ Super Node 1 => [tex]I_4\,+\,I_3\,=\,I_1\,+\,I_2[/tex]

When I combine these equations to get 4 equations with 4 variables, I get the following matrix:

[tex]\left[\begin{array}{cccc|c}
-1 & 1 & 0 & 0 & -10 \\
0 & -1 & 1 & -5 & 0 \\
1 & 0 & -1 & 5 & 10 \\
\frac{1}{2} & \frac{1}{4} & \frac{1}{3} & 0 & 0
\end{array}\right][/tex]

The columns go like this: v1, v2, v3, I, constant

But this matrix has infinte solutions! How do I solve?
 
Last edited:

Answers and Replies

  • #2
489
0
I figured it out!

The last variable column of the matrix can be eliminated because [tex]I\,=\,\frac{v_1}{2\Omega}[/tex]

This gives the matrix:

[tex]\left[\begin{array}{ccc|c}-1 & 1 & 0 & -10 \\-\frac{5}{2} & -1 & 1 & 0 \\ \frac{7}{2} & 0 & -1 & 10 \\ \frac{1}{2} & \frac{1}{4} & \frac{1}{3} & 0 \end{array}\right][/tex]

This RREF's out to:

[tex]v_1\,=\,\frac{70}{23}\,=\,3.043\,V[/tex]

[tex]v_2\,=\,-\frac{160}{23}\,=\,-6.956\,V[/tex]

[tex]v_3\,=\,\frac{15}{23}\,=\,0.6522\,V\,V[/tex]

NOTE: The third row of the matrix is not required!
 
Last edited:

Related Threads for: CIRCUITS: Current Controlled Voltage source, Indep. Voltage source, Four resistors

Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
20
Views
3K
Replies
9
Views
677
Replies
3
Views
123
Replies
17
Views
845
Top