Ohms law: V = I * R only works at an instant in time. Since you are talking about an AC circuit, voltage and current are changing all the time. If you take a sample of voltage, it could be anywhere from 311 volts (220*sqrt(2)) to -311V. When we talk about 220 volt circuits, we are talking about RMS voltage (a type of average). Now assume you sampled the voltage at the moment it crosses zero volts. You would expect to see 0 current and as a result 0 watts (P = V * I). But 1/100th (2* 50Hz) of a second later, the voltage would be at its maximum (or minimum). Now if you sampled the voltage and current at that moment, you would get a very different calculation of wattage.
So to accurately determine wattage, you must simultaneously sample voltage and current multiply them together and sum thousands of these over one 50Hz cycle. This will be the wattage of your appliance.
A less accurate method is to measure with an RMS meter, the RMS voltage and current and multiply them together. For a purely resistive load like an incandescent the two methods are the same. But many household loads are not purely resistive. A laptop power supply, refrigerator, hairdryer, TV, are all reactive to some degree. Look at the screen shots I posted here:
The hot air gun (hair dryer on steroids) is very non-linear. Just using RMS V and I will not get you the right wattage.
So now that I have complicated your view of Ohm's Law, what are your goals? Do you want to know the exact wattage of something, or that appliance A is better than B? Do you want to know the peak current use, or the RMS? Do you care if your power sags bellow 220 RMS? What about the power factor (think of it as the difference between ideal resistive power use and your actual use)?
One solution is to just assume that your voltage is always at 220 and also assume your appliance is resistive. Then you can pass the output of your sensor through an RMS to DC converter chip http://www.analog.com/en/special-linear ... index.html
that will give you a DC voltage proportional to the RMS current. This you can "multiply by 220" to get wattage. This avoids the high frequency sampling.
The above explanations are somewhat simplistic. They are meant to convey concepts not necessarily absolute truth.
PS: And attached is a current plot of a switching power supply. Notice how the current draw is not sinusoidal like a light bulb. The current spikes up as the voltage nears its peaks.
It was brought to my attention that some of my numbers are wrong. Specifically the timing of a 50Hz wave. The time for a full cycle is 0.020 seconds or twenty milliseconds. The time from a zero crossing to a peak is 1/4 of 20 milliseconds or 1/200 (5 ms) not the 1/100 that I stated. I had divided by two not four. Glad I have an editor watching over me!
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