How Do You Calculate Average and RMS Values for a Half-Wave Rectified Signal?

[Machodog]

Homework Statement

A sinusoidal voltage waveform is rectified so that it becomes a half-wave waveform (i.e. the bottom half has been "chopped off"). Determine:

i) The average p.d.
ii) The RMS p.d.
iii) The heat dissipated in a 200ohm resistor in 100s

Homework Equations

$P_{avg} = \frac{(V_{rms})^2}{R}$

The Attempt at a Solution

I'm not sure, but I would guess that the average p.d. is the line that cuts the rectified waveform in such a way that the area above and below is the same. I have a vague recollection about it being $\frac{2}{\pi}$ times the peak voltage.
I am also quite uncertain about the RMS, how would the voltage being zero half the time affect this value? I'm guessing it will no longer be $\frac{\sqrt2}{2} V_{peak}$.

Please could anyone give me some clues on how to work out the RMS and average values?EDIT:Oops sorry I did not mean to post the same thread twice...just ignore the other one!

 

[Delphi51]

I don't know of any formula for the half-wave signal. I rather think you will have to find out what "root mean square" means and work it out from the definition - no doubt you will be integrating over a full wavelength (the V = zero part will be easy!).

The average potential will be the same sort of thing, the area divided by the time.

 

[nlightner]

Hello,

I can provide some insight on how to approach this problem.

First, let's define some terms. The average p.d. refers to the average potential difference, or voltage, across the resistor. This can be calculated by finding the area under the rectified waveform and dividing it by the time period.

To find the RMS p.d., we need to first understand what RMS stands for. It stands for Root Mean Square, which is a mathematical way of finding the effective value of a waveform. In other words, it is the equivalent DC voltage that would produce the same amount of heat in the resistor as the AC waveform. To calculate this, we need to square the voltage at each point in the waveform, find the average of these squared values, and then take the square root of that average. This can be simplified for a half-wave rectified waveform by only considering the positive half of the waveform.

Finally, to calculate the heat dissipated in the resistor, we can use the formula P = V^2/R, where V is the RMS p.d. and R is the resistance of the resistor. This will give us the power dissipated in watts, which can then be multiplied by the time in seconds to get the total heat dissipated in joules.

I hope this helps guide you towards finding the solutions to this problem. Remember to always start by understanding the concepts and definitions before attempting to solve the equations. Good luck!