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Maximum power theory in electronics

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Please see my attachment. From the circuit
    Energy transferred to the load E = Ir + IR, where r is the internal resistance and R is Load Resistance. so
    I = E/(r+R)

    2. Relevant equations



    3. The attempt at a solution
    The Power W is W = I2R = E2R/(r+R)2
    Upto this i understand. I can't understand the following steps
    As R changes, so does W. W will be maximum when dW/dR is zero
    that is d/dR(E2R/(r+R)2) = 0
    My question is why W is maximum when dW/dR = 0. Why dW/dR concept is introduced here
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    Last edited by a moderator: Sep 22, 2011
  2. jcsd
  3. Sep 22, 2011 #2

    gneill

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    Staff: Mentor

    It's the basic calculus method for minimizing or maximizing a function. Take the derivative of the function with respect to the variable you wish to minimize (or maximize) with respect to, set the derivative equal to zero and solve for that variable. The resulting value(s) of the variable will either minimize or maximize the function.
     
  4. Sep 22, 2011 #3
    Thanks gneill. But, can't this maximum theory be explained by any other concept other than calculus method. I can't understand this method.
     
  5. Sep 22, 2011 #4

    gneill

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    Staff: Mentor

    Well, you could graph the function with respect to r and visually see the maximum :smile:
     
  6. Sep 23, 2011 #5
    Thanks Gneill.
     
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