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Superposition problem 2

  1. Feb 27, 2007 #1
    Find the total amount of current flowing through R3 in the circuit below.

    I mainly have doubts whether the answer given in the book is correct, to me it doesnt seem correct. Heres my attempt anyway.


    Make VS1 a short.

    Rt = R1//(R2//(R3+R4)
    (R1 is in parallel with R2 which is in parallel with the series combination of R3 and R4).

    Rt = 680//(220//(330+470) = 680//(220//800) = 680//172.54 = 138.89ohms

    Total current flowing from current source = 100mA

    IR3 = Rt/(R3+R4) * IS = 139/800 * 100mA = 17mA

    Current is flowing left to right over R3.

    Make IS an open as it is a current source.

    Rt = R2 + ((R3+R4)//R1)
    (R3 and R4 are in series, this combination is in parallel with R1, R2 is in series with the rest of the circuit.)

    Rt = 220 + (800//680) = 587

    It = Vs1/Rt = 20/587 = 0.034A or 34mA

    IR3 = Rt / (R3+R4) * It = 587/800 * 0.034 = 0.025A or 25mA
    (i chose R3+R4 as the current flowing through a series combination is the same.)

    As the polarity of both sources is the same (current flowing in same directions). The total current across R3 = 42mA

    If there are any errors could someone please indicate them to me, any help would be very much appreciated.
  2. jcsd
  3. Feb 27, 2007 #2
    the back of the book says 1.6mA is flowing through R3, to me doesnt seem to make any sense.
    Last edited: Feb 27, 2007
  4. Feb 27, 2007 #3


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    Staff: Mentor

    A good way to cross-check your answer would be to write the two KCL equations for the two sides of R3, and solve for the voltages and the resulting R3 current. What answer do you get when you solve this with straight KCL equations?
  5. Feb 27, 2007 #4


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    No, the polarity of Vs1 makes the current in R3 negative, so you must subtract the currents.
    The rest of your reasoning is correct, so if did not make any mistake in the calculations, the answer should be -8mA.
  6. Feb 27, 2007 #5
    So am I right in assuming the 1.6mA is not the correct answer? Im fairly sure that my calculations are correct, I will have another look. Thank you SGT for your pointers on series parallel relationships, the final cog turned this morning! Does anyone have any recommended texts that mainly focus on problems and worked solutions? I have lots of theory books but not enough problems to work my way through.
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