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# Why voltage is 11kv, 22kv, 33kv, 110kv, 220kv...?

Due to the form factor=1.11, so output voltage must be multiply of form factor, so we get 11,22,33. First let us define form factor before we go into the question:

The form factor of an alternating current waveform (signal) is the ratio of the RMS (Root Mean Square) value to the average value (mathematical mean of absolute values of all points on the waveform). In case of a sinusoidal wave, the form factor is approximately 1.11.

The reason is something historical. In olden days when the electricity becomes popular, the people had a misconception that in the transmission line there would be a voltage loss of around 10%. So in order to get 100 at the load point they started sending 110 from supply side. This is the reason. It has nothing to do with form factor (1.1).

Nowadays that thought has changed and we are using 400 V instead of 440 V, or 230 V instead of 220 V. Also alternators are now available with terminal voltages from 10.5 kV to 15.5 kV so generation in multiples of 11 does not arise.

Transformer voltage E=4.44 f A B N, in which the factor 11 is included

Of these, only N (number of winding turns) needs to be an integer. A is the core cross-section area, in square meters, so that is very rarely an integer, but mostly a tiny fraction of a square meter. B is the magnetic field strength, in Wb/m^2, so that does not have to be integer either. Lastly f (frequency, in Hz), that does not have to be integer either; we only need to listen to the chromatic scale of notes on a piano, or a guitar. In power supplies, yes, it is most often either 50 Hz or 60 Hz, but that is not a requirement for generating any voltage, different from the multiples of 1.1, as mentioned.

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