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Homework Help: Current in parallel circuits

  1. Feb 19, 2007 #1
    This is just a general question... when trying to solve for the current in each resistor in a parallel circuit, how do you go about setting it up? (I know that the equation V=IR comes in handy...)
     
  2. jcsd
  3. Feb 19, 2007 #2

    ranger

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    You could use the current divider rule. That would require you to find the total current in the circuit. Whats wrong with using V=IR?
     
  4. Feb 19, 2007 #3
    What is the current divider rule?
     
  5. Feb 19, 2007 #4

    ranger

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    Its used to find current when resistances are hooked up in parallel with each other. Here is a wiki picture that should clear things up for you:
    http://upload.wikimedia.org/wikipedia/en/4/47/Cdr.GIF [Broken]
     
    Last edited by a moderator: May 2, 2017
  6. Feb 19, 2007 #5
    That really helped! But if the circuit has three branches in parallel, does the formula change to I1=Itotal x ((R2+R3)/(R1+R2+R3)) ?
     
  7. Feb 19, 2007 #6

    ranger

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    It changes a little when we have more than two resistances. Lets consider a circuit with three parallel branches. We know that the voltage drop across any resistor in a parallel circuit is equal to that of the source:

    [tex] I_x = \frac{V_s}{R_x}[/tex]

    [tex]V_s = I_TR_T[/tex] <--the source voltage is equal to the total current times the total resistance.

    Now substituting [itex]I_TR_T[/itex] for Vs in the first equation (Ix).

    [tex]I_x = \frac{I_TR_T}{R_x}[/tex]

    We can therefore conclude that the current through any parallel resistor is in fact:
    [tex]I_x = \frac{R_T}{R_x}\cdot I_T[/tex]

    Hope it helps/
     
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