My Math Forum Average Power help

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 December 2nd, 2012, 01:35 AM #1 Newbie   Joined: Dec 2012 Posts: 2 Thanks: 0 Average Power help Show that: P(ave.) = Im*Vm(cos?)/2 WHERE: i=Im*sin?t v=Vm*sin(?t+?) ==> sin(?tcos? + sin?*cos?t hint: P = v*i (instantaneous power) P(ave.) =1/T?0^T P.dt (integrated from 0 to T) please help guys... thanks.
 December 3rd, 2012, 07:38 PM #2 Senior Member     Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 Math Focus: Electrical Engineering Applications Re: Average Power help $wT=2 \pi \ so \ T=\frac{2 \pi}{w}$ $P(ave)=Im \cdot Vm \cdot \frac{w}{2 \pi}\int_0\,^{\frac{2 \pi}{w}}\sin(wt) \cdot \sin(wt+\phi) \ dt$ $\sin(wt) \cdot \sin(wt+\phi)=\frac{1}{2}\left(\cos(\phi)-\cos(2wt+ \phi)\right)$ $P(ave)=Im \cdot Vm \cdot \frac{w}{4 \pi}\int_0\,^{\frac{2 \pi}{w}}\left(\cos(\phi)-\cos(2wt+ \phi)\right) \ dt$ $P(ave)=Im \cdot Vm \cdot \frac{w}{4 \pi}\left. \left(\cos(\phi) \cdot t-\frac{\sin(2wt+\phi)}{2w}\right)\right|_0^{\frac{2 \pi}{w}}$ Can you take it from here? The second term should cancel when evaluated.

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