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Resistor Heat Dissipation (with imaginary numbers)

  1. Nov 29, 2011 #1
    Friends:

    I am wondering about heat dissipation when you have imaginary numbers.

    Lets say a current I = (3 + 4j) Amps is going through an impedance Z = (2 + 3j) Ohms. What is the amount of heat dissipated by the impedance?

    I think that you take the magnitude of the current, |I| = 5 Amps, and then find the heat dissipated by only the real part of the impedance, Re(Z) = 2. The heat dissipated would be P = (5^2)*2 = 50 W.

    Is this correct?

    Note: This is not a homework question. This is something I just wanted to verify.
     
  2. jcsd
  3. Nov 30, 2011 #2

    I like Serena

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    Homework Helper

    The RMS power is:
    [tex]P_{RMS}={|I|^2 \over 2} |Z|[/tex]
     
    Last edited: Nov 30, 2011
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