The basic
principle of the ac generator is a direct consequence of Faraday's law of
induction. When a conducting loop is rotated in a magnetic field at constant
angular frequency ω a sinusoidal voltage (emf) is induced in the loop. This
instantaneous voltage is,

V = V

_{0}sin ωt ... (i)**AC generator in action**

The usual circuit diagram
symbol for an ac source or generator is shown in Figure.

Another video to explain how AC Generator Works

In Equation (i) V

_{0}is the maximum output voltage of the ac generator, or the voltage amplitude and w is the angular frequency, equal to 2π times the frequency f.
ω = 2πf

The frequency of ac in India is
50 Hz, i.e.,

f = 50 Hz

So,
ω = 2πf » 314 rad/s

The time of one cycle is known
as time period T, the number of cycles per second the frequency f.

T = 1/f or T = 2π/ω

A sinusoidal current might be
described as,

i = i

_{0}sin ωt
If an

**alternating current**is passed through an ordinary ammeter or voltmeter, it will record the mean value for the complete cycle, as the quantity to be measured varies with time. The average value of current for one cycle is,
Thus,

_{one cycle}= 0
Similarly, the average value of
the voltage (or emf) for one cycle is zero.

_{one cycle}= 0

Since, these averages for the
whole cycle are zero, the dc instrument will indicate zero deflection. In ac,
the average value of current is defined as its average taken over half the
cycle. Hence,

This is sometimes simply
written as, i

_{av}. Hence,
i

_{av}=_{Half Cycle}= 2/π i_{0}≈ 0.637 i0
Similarly, V

_{av}= (2/π)V_{0}≈ 0.637 V_{0}
A dc meter can be used in an ac
circuit if it is connected in the full wave rectifier circuit. The average
value of the rectified current is the same as the average current in any half
cycle, i.e., 2/π time the maximum current i

Similarly, we get RMS value V

_{0}. A more useful way to describe a quantity is the root mean square (rms) value. We square the instantaneous current, take the average (mean) value of i^{2}and finally take the square root of that average. This procedure defines the root-mean-square current denoted as irms. Even when i is negative, i^{2}is always positive so irms is never zero (unless i is zero at every instant). Hence,Similarly, we get RMS value V

_{rms }= V_{0}/√2 ≈ 0.707 V_{0}
The square root of the mean
square value is called the virtual value and is the value give by ac
instruments.

Thus, when we speak of our
house hold power supply as 220 volts ac, this means that the rms voltage is 220
volts and its voltage amplitude is,

V

_{0}= √2V_{rms }= 311 volt**Form Factor**

The
ratio, rms value/average value = (V

_{0}/√2)/(2V_{0}/π)
is known as form factor,

**Note:**

1. The average value of sin wt,
cos wt, sin2wt, cos2wt, etc. is zero because it is positive half of the time
and negative rest half of the time. Thus,

= i

_{0}sin (ωt ± f), V = V_{0}sin (ωt ± f)
or i = i

_{0}cos (ωt ± f), and V = V_{0}cos (ωt ± f)