Need help with Alternating Current?

Question

I have tried to figure this question out, but can't seem to get the right answer...If someone can answer this, or even simply give me the formula needed, I would be grateful! Here is the question:

An alternator provies 20A of Peak current at 100 Volts Peak AC to a resistive electric heater. How much heating power is delivered to the load?

Thank you all very much!! I was about to give up on this one....thank you again!

Answer 1

It was always helpful to me to remember that the 120 volts that you receive at your house always references the effective voltage, not the peak voltage. If we refered to our house voltage in terms of its amplitude (peak), the value would be 120 * 2^0.5 or 169.7 volts.

But as my old textbook explains it, the effective value of a particular sinusoidal voltage is the value of the dc voltage required to supply the same amount of power to a load. Therefore, to convert a sinusoidal current or voltage from peak to effective, divide the peak value by 2^0.5

Since both of these are measured in peak values, the amount of power delivered would be
p=20A/2^0.5 * 100 V/2^0.5

or 2000/2 watts = 1000 watts

Answer 2

Power = effective voltage x effective amperage =
{100 V / root(2)) x (20 A / root(2)} = 200 W / 2 = 100 watt

Th

Answer 3

Convert the peak values to there effective rms values
The root-mean-square value of a sine wave is 70.7% of the peak value.

So, to convert peak value to rms value, multiply by peak value by 0.707