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Kirchhoff's Rules. Solving for currents in circuit with two batteries

  1. Aug 31, 2013 #1
    1. The problem statement, all variables and given/known data

    zAhzBia.png

    What are the sizes and directions of the currents through
    resistors (a) R2 and (b) R3 in Fig. 27-42, where each of the three resistances is 4.0 Ω?

    2. Relevant equations
    ΔV=IR


    3. The attempt at a solution
    Equations:
    1) ΔVB2 -(i1)R1 -(i2)R2 -ΔVB1=0
    5V - 4(i1) - 4(i2) =0
    4(i2)=5V -4(i1)

    2) ΔVB2 -(i1)R1 -(i3)(R3)=0
    10V -4(i1) -4(i3) =0
    -4(i3)=-10V + 4(i1)

    not sure about this one
    3) ΔVB1 -(i2)R2 -(i3)(R3)=0
    5V + 4(i2) -4(i3) =0

    4) i1=i2 + i3

    5V +5V -4(i1) -10V +4(i1)=0
    0=0

    I'm not really sure what to do here.
     
    Last edited: Aug 31, 2013
  2. jcsd
  3. Aug 31, 2013 #2

    ehild

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    Gold Member

    The blue equation is not independent from the previous ones. Use eq.4 to find i1.

    ehild
     
  4. Sep 1, 2013 #3

    rude man

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    I also suggest superposition:
    solve for the currents with one battery shorted, solve with the other battery shorted, then add the results.
     
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