Why this is wrong?

Discussion in 'Homework Help' started by screen1988, Mar 17, 2013.

  1. screen1988

    Thread Starter Member

    Mar 7, 2013
    310
    3
    Please see attached file.
    Assuming that all values are known. Now I need to compute i_{1}
    I can caculate i_{1} easily by using KVL, KCL laws but I wonder why the method that I did don't work.
    In this case, I consider current source ideal and therefore it has infinitive resistance. Hence, the combined resistance of R_{2} and current source is equal to R_{2}. The combined resistance of the circuit will be  R{1} + R {2} and the current i_{1} =\dfrac {V} {R_{1}+R_{2}}. I know this is wrong but I cann't explain it. Hope anyone could help me out.
     
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  2. MrChips

    Moderator

    Oct 2, 2009
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    It is true that the combined resistance of R1 and R2 is R1 + R2.
    But the current in R2 is not i1.

    By KCL, the current in R2 = i1 + I.

    By KVL, V = i1R1 + (i1 + I)R2.
     
  3. screen1988

    Thread Starter Member

    Mar 7, 2013
    310
    3
    Thanks, MrChips!
    Do you meant that the model of resistor R2 and current source as a resistor is wrong?
    If this is correct, then i1 has to equal V/(R1+R2).
     
  4. MrChips

    Moderator

    Oct 2, 2009
    12,415
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    i1 is not equal to V/(R1 + R2).
    This assumes that the voltage across R2 is i1 x R2 which is incorrect.
    The voltage across R2 is (i1 + I) x R2.

    You must take into account I.
     
  5. WBahn

    Moderator

    Mar 31, 2012
    17,715
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    I'm confused by this claim. R1 and R2 are not in series, so what does the combined resistance R1+R2 represent?

    I would recommend taking R2 and the current source and converting them into a Thevenin equivalent. Then you have two voltage sources and two resistors all in series and finding the current is trivial (provided care is taken to get the polarities of the sources correct).
     
  6. MrChips

    Moderator

    Oct 2, 2009
    12,415
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    Sorry. I suspected you would come back and get me for this. I retract my statement.

    The op is trying to assume the model of the current source is one with infinite resistance.
    He forgot to include the value of I.

    The voltage across R2 is (i1 + I)R2.
    This is equal to i1 x R2 if I = 0. In which case, R1 and R2 combined is R1+R2 if and only if I = 0.
     
  7. WBahn

    Moderator

    Mar 31, 2012
    17,715
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    We do tend to keep each other honest, don't we?:p
     
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