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Homework Help: Two batteries and three resistors

  1. Feb 13, 2010 #1
    1. The problem statement, all variables and given/known data
    This is the drawing for the problem
    The two questions are:
    1) How much current flows through 6.0 V battery when the switch is closed?
    2)How much current flows through 6.0 V battery when the switch is open?

    2. Relevant equations
    Kirchoffs rules (charge conservation and loop rule)

    3. The attempt at a solution
    I attempted to set up two loops to solve for the current, the first one going around the outside and solving for I3:
    0 = 6V - I1R1 - I3R3
    I3 = 6V - 5/2I1
    Then setting the second loop around the left side of the diagram and solving for I2:
    0 = 9V - I1R1 + I2R2
    I2 = 9V - 5/4I1

    Then using I1 - I2 - I3 = 0 and plugging in the equations above and solving for I1, which I found to be 3.16 A, then continuing to algebraically solve and find I3 as -1.9A and I2 as 5.05 A.

    From this point, I am not sure what to do or even if I got the above numbers correct. I tried adding I1 and I3 because that would be the loop that would be used for the 6V if the switch is closed, but that is not correct (1.26 A)

    I could use some guidance, thank you very much in advance!
  2. jcsd
  3. Feb 13, 2010 #2
    If you have the currents then you can go back and see if in fact that the sum of the voltage drops around any loop is zero.

    The physics text by Halliday and Resnick does a similar problem as an example.
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