Question

the average value of an alternating current is zero yet the square root of the average squared value is not zero. Explain why?

Answer 1

it's more of a concept than mathematics. for example when an AC current is passed thru a conductor , it gets heated up naturally suggesting that some of the energy has spent in heating the conductor but when you find the area under the curve , it gets exactly cancelled suggesting no consumption of energy during transmission.

hence this anomaly is solved by taking root mean square (RMS) value for AC current