1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

CIRCUIT ANALYSIS: 3 resistrs, I src, V src, V.C.V.S. in series w/ resistor - Find V_A

  1. Jan 22, 2007 #1
    1. The problem statement, all variables and given/known data

    Use nodal analysis to find [itex]V_A[/itex] in the circuit below.

    [​IMG]


    2. Relevant equations

    KVL, KCL, v = i R, super-node?


    3. The attempt at a solution

    I made a few currents and showed the obvious KVL loop.

    [​IMG]

    [tex]V_1\,=\,V_A[/tex] <---- Right?

    [tex]I_1\,=\,\frac{V_1\,-\,0}{2\Omega}[/tex]

    [tex]I_2\,=\,\frac{V_3\,-\,0}{16\Omega}[/tex]

    [tex]I_3\,=\,\frac{V_1\,-\,V_2}{4\Omega}[/tex] <------Right?


    I know KCL for [itex]V_1[/itex]:

    [tex]\frac{30\,-\,V_1}{1\Omega}\,=\,\frac{V_1\,-\,0}{2\Omega}\,+\,\frac{V_1\,-\,V_2}{4\Omega}[/tex]

    [tex]7\,V_1\,-\,V_2\,=\,120[/tex]


    I know KCL for [itex]V_3[/itex]:

    [tex]\frac{V_1\,-\,V_2}{4\Omega}\,+\,3\,=\,\frac{V_3\,-\,0}{16\Omega}[/tex]

    [tex]4\,V_1\,-\,4\,V_2\,-\,V_3\,=\,-48[/tex]


    For KVL1:

    [tex]-V_1\,+\,4\,I_3\,+2\,V_A\,+\,V_3\,=\,0[/tex]

    [tex]2\,V_1\,-\,V_2\,+\,V_3\,=\,0[/tex]


    Now, putting those three EQs into a matrix and rref:

    [tex]\left[\begin{array}{cccc}7&-1&0&120\\4&-4&-1&-48\\2&-1&1&0\end{array}\right]\,\,\longrightarrow\,\,\left[\begin{array}{cccc}1&0&0&\frac{648}{29}\\0&1&0&\frac{1056}{29}\\0&0&1&-\frac{240}{29}\end{array}\right][/tex]

    This gives me [itex]V_1\,=\,V_A[/itex] equal to 22.34 V.

    Thanks for the help mjsd!
     
    Last edited by a moderator: Apr 22, 2017 at 3:18 PM
  2. jcsd
  3. Jan 22, 2007 #2

    mjsd

    User Avatar
    Homework Helper

    all your equations look sound to me..
     
  4. Jan 22, 2007 #3

    mjsd

    User Avatar
    Homework Helper

    oh..hang on.... 2nd line for KCL for V3 is wrong where is the 48 gone?
     
  5. Jan 22, 2007 #4
    Corrected, thanks much!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: CIRCUIT ANALYSIS: 3 resistrs, I src, V src, V.C.V.S. in series w/ resistor - Find V_A
Loading...