Vrms derivation: half wave

Discussion in 'Homework Help' started by makepeace, Nov 10, 2012.

  1. makepeace

    Thread Starter New Member

    Nov 10, 2012
    1
    0
    Hi,

    This is from an old thread:

    I'm having a little bit of trouble with understanding the derivation for the Vrms of a half wave sinusoidal voltage.

    As I see it, you cannot use Vp*sin(wt) as your V(t) if you are using 2pi/w as your period, because for half the period, V(t)=0.

    The function V(t) is a piece function where:

    V(t)=Vp*sin(wt) where 0 < t < pi/w
    and
    V(t)=0 where pi/w < t < 2pi/w

    Could someone please explain why the V(t) = 0 part is neglected?

    Thanks
     
  2. The Electrician

    AAC Fanatic!

    Oct 9, 2007
    2,285
    330
    You'll notice that in the expression for full-wave, there is a factor of 2/T in front of the integral; for half-wave, there is a factor of 1/T in front of the integral. Since the value of the integral would be the same for the interval 0<t<T/2 as for T/2<t<T (by symmetry), t_n_K simply did the integration over half the interval and multiplied by 2 to take care of the full-wave case.
     
  3. crutschow

    Expert

    Mar 14, 2008
    13,056
    3,245
    It makes sense that a half-wave would have 1/2 the power of a full-wave sinewave. ;)
     
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