**(New tips are continually
added to these pages. Check back in a few months' time for more)**

**TOPIC
12: Alternating Currents and Rectification**

__Tip 1:__

How to find root-mean-square voltage or current? The procedure is to square the waveform first, then find the mean, then finally root the mean.

The r.m.s value of standard waveforms have to be memorised, eg.

Normal Sine/ Cosine Wave:
*V*_{rms} = *V*_{o}/Ö2

Full-Wave Rectified
Sine/Cosine Wave: *V*_{rms} = *V*_{o}/Ö 2

Half-Wave Rectified
Sine/Cosine Wave:
*V*_{rms} = *V*_{o}/ 2

Direct Current:
*V*_{rms} = *V*_{o}

Square Wave with Max. at
*V*o and Min. at -*V*o: *V*_{rms} = *V*_{o}

Pulse Train with Pulse
Width *W* and Period *T*: *V*_{rms} = (Ö(*W*/*T*)*V*_{o}

For more complex waveforms, there are 2 methods to find the r.m.s.

__Method 1 (Integration)__

First, square the
waveform. Then integrate the squared waveform to find the area under the
graph. Next divide the integral by the period to find the mean.
Finally, root the mean to get *V*rms.

__Method 2 (Cut-And-Paste
Method or what I call the Ice Cream Method)__

Let's use the normal sinusoidal waveform as our example (refer to animations below).

Step 1: Draw
the original sinusoidal graph *V* = *V*_{0} sin * wt*
(the Red one).

Step 2: Square this
graph to get *V*^{2} = *V*_{0}^{2} sin^{2}
* w t*
(the Green one).

Step 3: Imagine that the green squared graph are scoops of ice cream resting on a tray (the tray is the X axis).

Step 4: Turn on the oven to melt the green ice creams so that they become ice water (the blue line).

Step 5: The blue line is
the mean of the squared graph. In our example, the height
of the ice cream is *V*_{0}^{2} so half the height (the mean) is
*V*_{0}^{2}/2.

Finally, root the mean
(*V*_{0}^{2}/2) to obtain *V*_{0}/Ö2
(proven).

You can try with other waveforms, eg. full wave rectified, half wave rectified, triangular, square, or saw-tooth waves.

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