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Homework Help: Calculating current in circuit with multiple emf's using Kirchhoff's

  1. Jul 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Circuit.jpg


    Find I_1, I_2 and I_3 if the switch, k, is closed using Kirchhoff's Rules.

    2. Relevant equations
    V=IR


    3. The attempt at a solution

    I've had multiple attempts at this and this one is the one that came closest to a solution.

    Setting up 3 equations:
    1) I_1 = 1_2 + I_3 => I_1 - I_2 - I_3 =0
    2) 12V + I_3*(4 Ohm) - I_1*(7 Ohm) = 0
    3) 12V - 9V - I_2*(5 Ohm) - I_1*(7 Ohm) = 0

    2) 12 = 7*I_1 - 4*I_3 => 12 = 7*(I_2 + I_3) - 4*I_3 => 12 = 7*I_2 + 3*I_3
    3) 3 = 7*I_1 + 5*I_2 => 3 = 7*(I_2 + I_3) + 5*I_2 => 3 = 12*I_2 + 7*I_3

    Getting rid of I_3:

    84 = 49*I_2 + 21*I_3
    09 = 36*I_2 + 21*I_3
    ---------------------------
    75 = 13*I_2

    I_2 = 5.75

    By substituting in, I get

    I_1 = -3.7
    I_3 = -9.5

    Is this anywhere near correct, I don't know why, but somehow this seems fishy to me :S
     
    Last edited: Jul 26, 2010
  2. jcsd
  3. Jul 27, 2010 #2

    collinsmark

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    Homework Helper
    Gold Member

    I think your first equation is not correct. Pay close attention to the direction of the arrows. See how the sum together at either center top node, or center bottom node. You'll find that

    I2 = I1 + I3

    (not, I1 = I2 + I3 that you originally had.)

    [Edit: Oh, and Spudnik, welcome to Physics Forums!]
     
    Last edited: Jul 27, 2010
  4. Jul 27, 2010 #3
    OK, I redid it with the new formula and I got

    I1=0.25
    I2=0.25
    I3=-2.5625

    Clearly this does not fit the initial equation I2=I1+I3

    It's strange though because those are the same values I got for I1 and I2 for part A) where it asked for the currents with the switch open...
     
  5. Jul 27, 2010 #4
    Double posting because I figured it out:

    I1= 72/83 A
    I2= -51/83 A
    I3= -123/83 A

    Using
    I2=I1+I3
    12+4I3-7I1=0
    12-9-5I2-7I1=0

    Setting them up for a matrix:

    I1 + I2 + I3 = Voltage
    +1 -1 +1 =0
    -7 +0 +4 =-12
    -7 -5 +0 =-3

    Letting the calculator do the rest for you: priceless.
     
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