Qucik Mesh Analysis KVL Question

Discussion in 'Homework Help' started by freemindbmx, Apr 30, 2014.

  1. freemindbmx

    Thread Starter Member

    Mar 5, 2014
    72
    0
    I posted the problem below. It appears the dependent source is inbtween two mesh's making it a super mesh I then need to make an AUX Equation showing Ix's relationship with the 10ohm resistor along with the super mesh's KVL.The only thing I want to make sure of is my super mesh equation and Auxiliary equation.

    Super Mesh:
    -(4Ω)I1 -(4Ω+20Ω)I2 + (2Ω)I3 -(20Ω)I4 = 0

    Aux Equation:

    2Ix=I4-I3

    Ix=I1-I4 (would be the correct relationship of the currents that equal Ix)?
     
  2. anhnha

    Active Member

    Apr 19, 2012
    773
    45
    There are four variables I1, I2, I3 and I4 and therefore, you need four equations.

    Super Mesh:
    4 (I2 - I1) + 20 (I2 - I4) + 2*I3 = 0
    Mesh I (top loop):
    5*I4 + 20 (I4 - I2) + 10 (I4 - I1) = 0
    Mesh II (loop on the left):
    10 (I1 - I4) + 4 (I1 - I2) = 12.3
    Last equation:
    2Ix = 2*(I1-I4) = I3 - I2
    Solving this, I get:

    I1 = 2.15
    I2 = 1.2
    I3 = 2.9
    I4 = 1.3
     
    Last edited: Apr 30, 2014
  3. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    Close, but not quite. A quick sanity check is to note that for the mesh for current In, the terms containing In is positive and the term containing all of the other currents are negative.

    In the case of this supermesh, the mesh currents are I2 and I3, so they should be positive while the terms for I1 and I4 should be negative.

    Look at your diagram again. Remember that when you have a supermesh involving currents Ia and Ib, the auxiliary equation needs to establish a relationship between Ia and Ib.

    Correct.
     
  4. freemindbmx

    Thread Starter Member

    Mar 5, 2014
    72
    0
    thanks, realized I messed up in writing down the Aux equation of 2Ix.For some reason I wrote down I4-I3 instead of I3-I2........Sorry for wasting time
     
  5. WBahn

    Moderator

    Mar 31, 2012
    17,715
    4,788
    No need to apologize, we all make mistakes all the time. The lesson is that it is worth your time to look for and adopt as many sanity checks as you can so that you can catch most of your errors. In school, this will help keep your grades up. In the real world, it will help keep you employed and possibly keep you from killing someone via an uncaught error.
     
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