Urms=1sqrtπsqrt∫α^πU^2sin^2θdθ

+∫0^αU^2sin^2θdθ)

where Urms is the root mean square (RMS) value of the voltage or current waveform, U is the instantaneous voltage or current, α is the maximum value of the angle θ (which can be π/2 for a half-wave rectifier or π for a full-wave rectifier), and the integral is taken over one cycle of the waveform.

The RMS value of a waveform is a measure of its effective or average value, and is used to calculate power in AC circuits. The formula for calculating power in an AC circuit is P=UrmsIrms, where P is power, Urms is the RMS value of the voltage, and Irms is the RMS value of the current.

In the formula given, the integral is taken over the range of angles where the waveform is non-zero, and the sine squared term accounts for the fact that the waveform is positive only in half of the cycle. The factor of 1/sqrt(π) is a normalization factor that ensures the RMS value is consistent with the definition of RMS as the square root of the mean of the squared values.

Overall, the formula provides a way to calculate the RMS value of a waveform in terms of its mathematical description, and can be used to analyze and design AC circuits