I am trying to determine the continuous effective power at my load resistor. I plot the following expression:
but this doesn't produce the results I am looking for. When I plot the next expression:
I get the expected curve. Why is there a difference between the two?
The difference occurs due to the point at which the RMS operator takes effect. In the first expression, the RMS is being calculated based on the instantaneous power of the resistor which would be equivalent to:
In the second expression, both the current and voltage have their RMS value calculated individually, and then the two RMS values are multiplied together. The second expression is the commonly accepted definition for determining power in AC circuits.