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Power in circuits

  1. Nov 7, 2005 #1
    In the circuit, E, R1 and R2 have constant values. However R has a variable value. FInd an epxression for R that results in the max power dissipation in that resistor.
    so do i do this
    [tex] i_{1} = i + i_{2} [/tex]
    [tex] E - i_{1} R_{1} - i_{2} R_{2} = 0[/tex]
    [tex] E - i_{1} R_{1} - iR = 0 [/tex]
    [tex] i_{2} R_{2} - iR = 0 [/tex]
    not too sure about the last one...
    and the power dissipation in that resitor is given by [tex] P = i^2 R [/tex] But to find the max power dissipation do i plug that expression for i back into the above expression and then differentiate OR sub i into this
    [tex] \frac{dP}{dR} = 2iR + i^2 [/tex]
    i used a sample value for i and got different values for the derivative. Which is correct?
    Please help!
     

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    Last edited: Nov 7, 2005
  2. jcsd
  3. Nov 9, 2005 #2

    BobG

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    You should use your Thevenin equivalent and Norton equivalent for this one - unless they're making you do this using differentiation and limits at least once just to make sure you truly appreciate Thevenin and Norton equivalents.
     
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