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Find current flowing through each resister, voltage across each resister and power

  1. Feb 2, 2010 #1
    1. The problem statement, all variables and given/known data


    Find current flowing through each resister, voltage across each resister and power consumed by each element in the following circuit.

    See the attachment


    2. Relevant equations



    3. The attempt at a solution

    The question I want to ask here is that is the current = 10 A? Because I got 2 answers for current, 0 A and 10 A.

    I did this:

    I combined 10 and 10 ohm resistors to get a 5 ohm resistor.
    Now total power consumed=total power supplied

    So I^2(3) + I^2(5) + I^2(2) = 100I
    which gives I = 0 or 10. Which one should I take?
     

    Attached Files:

  2. jcsd
  3. Feb 2, 2010 #2

    berkeman

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    Staff: Mentor

    Re: Find current flowing through each resister, voltage across each resister and powe

    I=0 is called the degenerate solution, and is not physical in this case. Use I=10.
     
  4. Feb 2, 2010 #3
    Re: Find current flowing through each resister, voltage across each resister and powe

    Ok but what is the reason again? What is degenerate solution ?
     
  5. Feb 2, 2010 #4

    vk6kro

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    Science Advisor

    Re: Find current flowing through each resister, voltage across each resister and powe

    If you add up the resistor values, you can get the total current flowing because you know the supply voltage.

    Then take this current and work out the voltage across each resistor and the power dissipated in it.

    With this circuit, you can tell by looking at it that zero current is not an option.
     
  6. Feb 2, 2010 #5

    berkeman

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    Staff: Mentor

    Re: Find current flowing through each resister, voltage across each resister and powe

    I apologize if I'm using and incorrect term there. I've been googling for a bit trying to find you a good definition, with very little luck so far. By degenerate solution, I meant when the variable x = 0 is a solution to an equation f(x) = 0, and it is a solution because all terms in the equation are zero. It's like multiplying both side of any equation by zero, and saying, yes, both sides are equal now.

    In your equation you had I on one side and all I^2 on the other. You should divide by I in that case, before solving the equation. If you do that, you will not end up with I=0 as a degenerate solution of the equation.
     
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