Vrms = 0.5 Vmax for Half Wave Rectifier: Proof

[songoku]

Homework Statement

How to prove that V_rms = 0.5 V_max for half wave rectifier

Homework Equations

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

 

[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 !