Maths of Electricity

Imagine a point moving on a circular path.Also consider the diameter. Connect the moving point and the diameter by a line . As the point circles, the line grows and diminishes both in the upper and lower halves. Now cut the lower-half and shift it by the length of the diameter. You get a wave like form. We can understand, as the point rotates, it can effectively produce waves in suitable environment.

In Maths,waves can be represented by sine or cosine function.
y=sin x
As x changes from 0-360 degree or 0-2pi radian (a full circle), y values oscillates like a wave as shown in figure. Now the sine function can be modified to suit our needs.
y=A sin 2pi n t
A- Amplitude- Maximum height of wave.
n- Frequency of rotation.
t- instant of time.

Next, imagine a coil of wire rotating inside and perpendicular to a strong Magnetic field. The Faraday's laws and Maxwell;s equations tells us that a electric voltage and current will be established in the coil. That current will be in wave form. That is, it will be increasing,decreasing and direction changing. It is the Alternating Current(AC). Producing AC is easy and also commercially viable.
In large scale, Power generation,the rotations(of Coil or Magnet) can be caused by wind, water flow, steam, Diesel engine etc.
For generated electric voltage, equations can be written as,
v=V sin 2pi n t
v- voltage at the time t
V- maximum voltage
n- Frequency of rotations or Alternating current

That is the "power " of Maths.

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