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Find currents and voltages - 2 batteries & 3 resistors

  1. Apr 20, 2016 #1
    1. The problem statement, all variables and given/known data

    upload_2016-4-20_22-13-18.png

    Find I1, I2, I3 as well as the voltages across each resistor.

    R1= 50 ohms
    R2= 220 ohms
    R3= 150 ohms

    2. Relevant equations
    Kirchhoff's loop law
    Kirchhoff's junction law


    3. The attempt at a solution
    Loop 1: Starting from the negative terminal of the 10V battery (ccw)

    10V - 50 (I1) - 220 (I2) = 0

    Loop 2: Starting from junction a (ccw). Note I added an I4 through R3 to try and make things easier for me to visualize .

    - 150 (I4) + 5 V + 0 (I3) + 220 (I2) = 0

    Junction law
    I1 = I2 + I4


    Loop 1
    10V - 50 I2 - 50 I4 - 220 I2 =0
    10V - 270 I2 - 50 I4 = 0

    Loop 2
    I2= (150 I4 - 5 V )/220 = 0.682 I4 - 0.0227 A

    Loop 1
    10V - 270 (0.682 I4 - 0.0227 A) - 50 I4 = 0
    - 234.14 I4 = -16. 129
    I4 = 0.069 A
    I2= 0.024 A
    I1= 0.093 A
    I3 = ???????

    Voltages across :
    R1 ==> 4.65 V
    R2 ==> 5.28 V
    R3 ==> 10.35 V


    I can't find I3. Is it possible that R2 "receives" a portion of I3 downstream (.....I5. ....) in addition to having I2 go through R2 it upstream? ???? Or maybe I3 is infinitely big (ideal wire model, goes from the positive terminal of the 5V battery and then directly to the negative terminal of the 10V battery)???
     
  2. jcsd
  3. Apr 20, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    I don't know why you've introduced I4. The branch has two components in series, so they MUST carry the same current, and that's already labelled I3.

    upload_2016-4-20_22-23-20.png
     
  4. Apr 20, 2016 #3
     
  5. Apr 21, 2016 #4
    Resolved.
     
    Last edited: Apr 21, 2016
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