# Is there really current in AC current?

Perhaps a simple question, but from the Wikipedia page, electric current is defined as"...a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire." (https://en.wikipedia.org/wiki/Electric_current)

So my question is then, how is it that AC current has amperage at all, if there is no net flow of electric charge? Is it caused by an equivalent power being generated somehow? If so, what is/are the equation(s) for finding that?

• Examine the title of your question and ask yourself what the xxxx you mean. Oct 10 '15 at 23:19
– Fizz
Oct 10 '15 at 23:22
• If that's too rich for you, also on the 1st page of goole hist you can find learn.sparkfun.com/tutorials/… or pbs.org/wgbh/americanexperience/features/general-article/… which have more "for dummies" expnanations. HTH.
– Fizz
Oct 10 '15 at 23:32
• @RespawnedFluff damn, I'm sorry you feel so strongly about that. If you'll notice, there is an answer below this conversation that helped me understand this. No need to be callous. I'm no adept at AC circuits (or most circuits, for that matter) but I am trying to learn. Sorry if the question was so dumb it offended you :( Oct 10 '15 at 23:49
• @DanielGomes, this site doesn't try to answer every question. We want to answer questions that can't be answered by a simple Wikipedia search. Oct 11 '15 at 1:05

In an AC system the mean voltage and the mean current are both zero but just because the mean of a quantity is zero doesn't mean that the quantity doesn't exist.

As an analogy consider two hydralic cylinders connected together by a pipe. I push one cylinder in and pull it out again. There was no net flow in the pipe but there was clearly flow when I was pushing the cylinder in and also flow in the opposite direction when I was pulling it out. If I place a load on one cylinder and move the other up and down i'm clearly using the flow of water to transfer power even though there is no net water flow.

Getting back to electricty consider a resistor connected to a sinewave AC power supply. For simplicity lets assume that our voltage source has a peak voltage of 1 unit and our resistor has a resistance of one unit. We can write equations for the instantaneous voltage, instantaneous current and instantaneous power.

V=sin(2πft)
I=V/R=sin(2πft)
P=IV=(sin(2πft))<sup>2</sup>


If we calculate the mean values of those functions we quickly see that V and I have a mean of 0 but P doesn't, it has a mean of 0.5.

So if our mean voltage and mean current are zero how do we meaningfully measure voltage and current? We use something called the "root mean square" value. That is we take the voltage or current waveform, square it, take the mean and then take the square root. Voltages and currents in AC power system are nearly always measured and discussed in RMS values.

We can use these RMS voltage and current values in the equations P=I2R and P=V2/R equations to calculate average power delivered to a resistive load.

It's tempting to also think we can apply RMS values to the P=IV equation but it is important to remember that this only applies if the voltage and current waveforms are proportional.

• Removed my last comment because it was dumb. Thanks @Peter Green for your great answer! Oct 11 '15 at 0:03