The ratio of mean value over ore half cycle to the rms value of a.c. of complete cycle

The ratio of the mean value over one half cycle to the RMS (Root Mean Square) value of an alternating current (AC) over a complete cycle is calculated as follows:

1. Mean Value of Half Cycle: The mean value of an AC over one half cycle is calculated by integrating the function over half a period and dividing by the half period. For a sinusoidal wave, this is 2/π times the peak value.

2. RMS Value of Complete Cycle: The RMS value of an AC over a complete cycle is calculated by squaring the function, averaging it over a period, and then taking the square root. For a sinusoidal wave, this is 1/√2 times the peak value.

3. Ratio: The ratio of the mean value over one half cycle to the RMS value of a complete cycle is then (2/π) / (1/√2) = √2/π ≈ 0.45.

So, the ratio of the mean value over one half cycle to the RMS value of an AC over a complete cycle is approximately 0.45 for a sinusoidal wave.