Cycle, period, frequency, average and rms

Cycle: One complete set of positive and negative values of an alternating quantity. It corresponds to 360° or 2π radians.

Time period (T): Time taken to complete one cycle, in seconds. T = 1/f.

Angular velocity (ω): Rate at which the rotating coil (or phasor) sweeps angle, in rad/s. ω = 2πf = 2π/T.

Frequency (f): Number of cycles completed per second, in hertz (Hz). In Nepal f = 50 Hz.

Average value: The mean of all instantaneous values over half a cycle (the full-cycle mean of a symmetrical wave is zero).

Iav = (1/π) ∫₀^π i dθ. For a sine wave, Iav = 2Im/π = 0.637 Im.

RMS (effective) value: The value of steady direct current that produces the same heating effect in a resistor as the alternating current does in the same time. It is the square root of the mean of the squares of the instantaneous values.

Irms = √[ (1/2π) ∫₀^{2π} i² dθ ]. For a sine wave, Irms = Im/√2 = 0.707 Im.