How are RMS current and mean current defined in AC circuits?

[saiaspire]

Hello people,

In an AC circuit, how is RMS current and Mean current defined as?
What is the practical meaning of RMS current?

Thanks in advance.

 

[Andrusko]

Well, in an AC circuit the current is alternating back and forth. So:

$$P = i^{2}R = (Isin(\omega t - \phi))^{2}R = I^{2}Rsin^{2}(\omega t - \phi)$$

This is the instantaneous rate at which energy is dissipated in the resistor. So the average rate at which energy is dissipated in the resistor is the average of this equation over time.

The average value of a sin^2 graph is 0.5. So:

$$P_{avg} = I^{2}R/2 = (I/\sqrt{2})^{2}R$$

So the quantity I/sqrt2 is called the root mean square or RMS value of the current I.

So if we use RMS current we can find the average rate of energy dissipation in an AC circuit.

This is what's usually used in electronics related work.