Root-Mean-Square Current and Voltage

The average current flowing through an element in an AC circuit is zero.

Prof:

The average voltage, like the current, is also zero.
The average power delivered by an AC circuit is not zero as any one who has been shocked by an AC circuit can attest.

AC ammeters and volt meters are designed to output the root-mean-square average of the current or voltage rather than the maximum values.
The difference between maximum and rms values of the current or voltage is just the square root of 2:

Prof:

One way to show that

with out doing any integrationis to first note that

This is true since both functions have the same shape, one is just the other translated by 1/4 of the period T along the t-axis.

Taking the average of the trigonometric identity,