Half wave rectifier proof

songoku

1. Homework Statement
How to prove that Vrms = 0.5 Vmax for half wave rectifier

2. Homework Equations

3. The Attempt at a Solution
I know the graph of half wave rectifier is just the upper part or lower part of sinusoidal wave. But I don't have clue to prove it..

Thanks

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JaWiB

So that means that for a half-wave rectifier you can define voltage as a piecewise function of time:
$$V(t) = \left\{ \begin{array}{cc}V_{max}sin({\omega}t),&\mbox{ if } 0 \leq t \leq \frac{T}{2}\\0,&\mbox{ if } \frac{T}{2} < t \leq T\end{array}\right.$$

And it's a fairly straightforward calculation to find the RMS value of the function:
$$\sqrt{\frac{1}{T}\int_{0}^{T}[V(t)]^2dt$$

songoku

I get it now

Thanks a lot, JaWiB !! Physics Forums Values

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