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Power in an AC Circuit Problem

  1. Apr 17, 2015 #1

    B3NR4Y

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    1. The problem statement, all variables and given/known data
    The circuit in operates at 60 Hz with Emax = 170 V, and R = 4.5Ω .
    How much energy is dissipated in the resistor in 0.75 s?
    2. Relevant equations
    P = VI
    For a circuit like mine with only a power source and resistor, the current and voltage are in phase, so
    V = E max sin (ωt)
    and
    [tex] I = \frac{E_{max} sin(\omega*t)}{R} [/tex]

    3. The attempt at a solution
    Since I want to know the power dissipated over time, I took an integral [tex] V_{0} I_{0} \int_{0}^{t} sin(\omega t) dt [/tex]
    this should give me the total energy dissipated at time t, it doesn't, and I am not sure why.
     
  2. jcsd
  3. Apr 17, 2015 #2

    rude man

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    You ignored your own expressions for V and I in forming your integral ...
     
  4. Apr 17, 2015 #3

    B3NR4Y

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    oh, jeez, it should be
    [tex] V_{0} I_{0} \int_{0}^{t} sin^{2}(\omega t) dt [/tex] ?
     
  5. Apr 18, 2015 #4

    rude man

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    Mucho better!

    BTW the integral is easier if you write it as VoIo/ω ∫sin2(ωt)d(ωt) with limits 0 to ωt.
    As if I'm not being picky enough, you should also use a dummy variable (like t') in the integral. ∫sin2(ωt')dt' with limits of 0 and t.
     
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