Vrms = 0.5 Vmax for Half Wave Rectifier: Proof

AI Thread Summary
For a half-wave rectifier, the voltage can be expressed as a piecewise function, where it equals Vmax*sin(ωt) for the first half of the cycle and 0 for the second half. To prove that Vrms equals 0.5 Vmax, one must calculate the RMS value using the integral of the square of the voltage function over one complete cycle. The calculation involves integrating the squared function from 0 to T/2 and normalizing by the period T. This leads to the conclusion that Vrms indeed equals 0.5 Vmax. The discussion highlights the mathematical approach to deriving this relationship.
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Homework Statement


How to prove that Vrms = 0.5 Vmax 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
 
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So that means that for a half-wave rectifier you can define voltage as a piecewise function of time:
<br /> V(t) = \left\{ \begin{array}{cc}V_{max}sin({\omega}t),&amp;\mbox{ if } 0 \leq t \leq \frac{T}{2}\\0,&amp;\mbox{ if } \frac{T}{2} &lt; t \leq T\end{array}\right.<br />

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

Thanks a lot, JaWiB ! :smile:
 

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