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Superposition Problem- Circuits

  1. Jun 19, 2013 #1
    1. The problem statement, all variables and given/known data
    2013-06-19193003_zpsc110ea7a.jpg

    For the above circuit, find the coefficients of the linear relationship vout = a1vs1 + a2is2 + a3is3 by superposition. Then find the power delivered to R3 when vs1 = 100 V, is2 = 2 A, and is3 = 4 A. Given: R1 = 20 Ω, R2 = 60 Ω, and R3 = 20 Ω.


    2. Relevant equations

    Ohm's Law: V = IR

    KVL: V1 + V2 + ... Vn = 0 for closed loops

    KCL: I1 + I2 + ... In = 0 going in an out of a node

    Voltage Division: V1 = Vsource * (R1/(R1+R2))


    3. The attempt at a solution
    I think I got the first two coefficients (though I could be incorrect). I found vout1 = vs1*(R3/(R1+R2+R3)) = 0.2Vs1 through voltage division. I'm pretty certain that's correct.

    I also found that vout2 = Is2*R3 = 20Is2, though I'm not quite as certain about that.

    But I absolutely cannot wrap my head around finding vout3 (when all independent sources are eliminated except Is3). I understand that in that situation, the Is2 branch essentially disappears and we are left with Is3 in parallel with a branch with R2 and a branch with R1 and R3, but we can't combine those since vout3 must stay isolated. I'm not sure what to do.
     
  2. jcsd
  3. Jun 19, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    You have a classic current divider scenario with current Is3 being divided between two branches. You know the total resistance of each of the branches.

    attachment.php?attachmentid=59714&stc=1&d=1371688705.gif

    Alternatively, consider converting Is3 and R2 to their Thevenin equivalent and finding the resulting current and then the potential across R3.
     

    Attached Files:

  4. Jun 19, 2013 #3
    So I want to use current division to find i2, then multiply that by R3 to get my voltage value?

    i2 = Is3*(R2/(R1+R2+R3))
    vout3 = i2R3
    vout3 = Is3*((R2*R3)/(R1+R2+R3))

    After substituting values in, vout3 comes out to be 12. Unfortunately either that or one of my previous solutions is wrong- a later part of the problem states that the total vout must be 100 V when vs1 = 100 V, is2 = 2 A, and is3 = 4 A. And (0.2*100) + (20*2) + (12*4) is 108. Did I go about finding vout3 the wrong way?
     
  5. Jun 19, 2013 #4

    gneill

    User Avatar

    Staff: Mentor

    Check your work for the coefficient for Is2.
     
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