A sinusoidal current is i = I₀ sinωt. The top trace shows the current; the lower trace shows the power, which is always positive and averages to half its peak. That is why the r.m.s. value, I₀/√2, is the steady current that would deliver the same mean power.
MissionPredict the r.m.s. value of a sinusoidal current whose peak value is I₀.Streak 0Best 0
The r.m.s. value of a sinusoidal current of peak value I₀ is:
peak current I₀5.0 A
r.m.s. current I₀/√23.54 A
frequency f , period T = 1/f50 Hz , 20 ms
mean power ÷ peak power0.5
The mean power is half the peak power, so the r.m.s. current is I₀/√2 and the r.m.s. voltage is V₀/√2.