# 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
2,300
335
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
13,475
3,361
It makes sense that a half-wave would have 1/2 the power of a full-wave sinewave.