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Homework Help: Calculating the current of a circuit- resistance and volatge known, see picture

  1. Jan 8, 2010 #1
    1. The problem statement, all variables and given/known data

    What current flows through the resistors R(1) = 1Ω, R(2) = 2 Ω and R(3) = 3 Ω, if the driving voltages are V(1) = 1V and V(2) = 2V?

    Picture:
    http://item.slide.com/r/1/151/i/lvtwIwH-0j8A8o-XAKDtPRQO1eHAb4Ik/ [Broken]

    2. Relevant equations

    V= RI → I= V/ R

    3. The attempt at a solution

    V(1)= I(2)R(2) + I(1)R(1)
    V(2)= I(3)R(3) – I(2)R(2)
    I(1)= I(2) + I(3)

    - From what I stated above, I conclude three equations:

    1) V(1) = I(2)R(2) + [(I(2) + I(3))*R(1)]
    2) V(2)= I(3)R(3) - I(2)R(2)
    3) V(1)= [I(2)*( R(1) + R(2))] + I(3)R(1)

    - I combined the three equations and simplify for the current that goes through ALL resistors, which in our case is I(3):

    I(2)= (I(3)R(3) - V(2))/ R(2)
    V(1)R(2)= [(I(3)R(3) – V(2))/ R(2))*(R(2) + R(1))] + I(3)R(1)R(2)
    (V(1)R(2))/ (R(2) + R(1))= (I(3)R(3)) + [I(3)R(1)R(2))/ (R(2) + R(1))]
    I(3)*[R(3) + (R(1)R(2)/ (R(2) + R(1))]= [V(1)R(2)/ (R(2) + R(1))] + V(2)

    I(3)= [(V(1)R(2)/ (R(2) + R(1)) + V(2)] / [R(3)* (R(1)R(2)/ (R(2) + R(1))]
    I(3)= 1.37 A

    Are my calculations correct?
    Thank you for helping!:smile:
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 8, 2010 #2

    diazona

    User Avatar
    Homework Helper


    Equation #3 here is the same as equation #1, just written slightly differently... so you really have only two independent equations. I'd just start from the original three you had above.

    I don't see where that last line comes from. The units are off, so something must be wrong in there.
     
    Last edited by a moderator: May 4, 2017
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