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Proof of current division

  1. May 16, 2007 #1
    My professor gave us the task of proving the current division law for two resistors in parallel. I know that the voltage across parallel resistors is the same, and that the sum of the branch currents adds to the sum of the total current.

    Here is the question:

    Prove that [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex] ; [tex] I_s[/tex] = the source current.

    Now, this is what I know: [tex] I_s= I_1 +I_2[/tex]

    That is about as far as I can get. I know that I need to manipulate [tex] I_s= I_1 +I_2[/tex] somehow to derive [tex]I_1= \frac{I_sR_2}{R_1 + R_2}[/tex].

    This is the first time I have ever been assigned a proof and I don't have any experience solving them, so my tool set is kind of lacking.

    As a side note I would like to be able to prove 'simple' theorems like this. I think it would give me a level of insight that I don't currently have.
     
    Last edited: May 16, 2007
  2. jcsd
  3. May 17, 2007 #2

    berkeman

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    Staff: Mentor

    I = V/R, correct? Please show us more work. Relax and focus.
     
  4. May 17, 2007 #3
    yes I = V/R so...

    [tex]I_s= \frac{V_s}{R_1} +\frac{V_s}{R_2}[/tex]

    It appears that the thing to do here is get rid of the fractions. I have done this on paper, but I am not seeing a critical relationship when I work through it.
     
    Last edited: May 17, 2007
  5. May 17, 2007 #4

    berkeman

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    Good. So write the equation for each leg....
     
  6. May 17, 2007 #5
    The equation for each leg? Well, each leg is just back to the current again. Right? [tex] \frac{V_S}{R_1} + \frac{V_S}{R_2} = I_1 + I_2[/tex].

    I'm running in circles!:cry:
     
  7. May 17, 2007 #6

    hage567

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    Homework Helper

    Try to work out an expression for Vs in terms of the total resistance of the circuit and Is (so find the equivalent resistance of two resistors in parallel).
     
  8. May 17, 2007 #7

    Fredrik

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    You can eliminate [itex]I_2[/itex] from the equation [itex]I_s=I_1+I_2[/itex], if you use the V=RI law to express [itex]I_2[/itex] as a function of [itex]I_1[/itex].
     
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