A Generator is a device which converts mechanical energy into electrical energy.
A.C Generator works on the principle of electromagnetic induction (motional emf). In generator an induced emf is produced by rotating a coil in a magnetic field. The flux linking the coil changes continuously hence a continuous fluctuating emf is obtained.
A.C Generator consists of the following parts.

Powerful field magnet with concave poles.


It is a rectangular coil of large number of turns of wire wound on laminated soft-iron core of high permeability and low hysteresis loss.

Slip rings:

The ends of the coil are joined to two separate copper rings fixed on the axle (S1 & S2).

Carbon brushes:

Two carbon brushes remain pressed against each of the rings which form the terminals of the external circuit.


In order to determine the magnitude and direction of induced e.m.f, let us consider the different positions of the coil which has ‘N’ turns of wire. In one revolution following positions can be considered.

When initially coil is vertical, the length arms AC and BD are moving parallel to the lines of force maximum number of lines link the coil, but rate of change of flux is zero, hence emf is zero.

As the coil moves from this position, sides AC and BD begin to cut the lines of force and induced emf is setup till it is maximum when the coil is horizontal. It has rotated 90o, 1st quarter is completed.

Further rotation decreases the value of emf, until at the end of 2nd quarter, when coil is vertical, it has rotated 180o, the emf is again zero.

As the coil rotates further from position 3 to position 4, an emf is again induced, but in reverse direction, because AC and BD are cutting the magnetic lines in opposite direction. The reverse emf reaches to –ve peak value at the end of 3rd quarter. The coil is horizontal and angle of rotation is 270o.

On further rotation, the emf again decreases and becomes zero when the coil returns back to its original position after rotating 360o.

This shows that the coil of generator produces induced emf which reverse its direction 2*f times in one cycle. Where f = frequency of rotation of coil.

Consider a coil ABCDA of ‘N’ turns rotating in a uniform magnetic field B with a constant angular speed ‘w’. Let the length of the coil is ‘l’ and its breadth is ‘b’.
To calculate emf in sides AC and BD we proceed as follows:

Motional emf = BvlSinq

Emf in side AC = BvlSinq = x1

Emf in side BD = BvlSinq = x2

Emf induced in the coil = x1 + x2

= BvlSinq + BvlSinq

x = 2 BvlSinq

If coil has ‘N’ turns, emf will increase N times

x = 2 BvlNSinq ----(1)

If angular velocity of coil is ‘w’ and it takes time ‘t’ to cover angle q then

q = wt also

V = rw and r = b/2

V = b/2w

Putting the value of q and V in eq. (1)

x = 2B (b/2w)lNsin(wt)

x = wB(b*l)sin(wt)

x = NBw(b.l)sinwt

x = NBwAsinwt –(2)

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this is the expression for the induced emf in the coil of an A.C generator at any instant.

If f = no. of rotation per sec. Then we have w=2pf

x = V = NBwAsin(2pft) – (3)

for maximum emf q = 90o or 270o

or 2pft = p/2 or 3p/2

and sin90o = sin p/2 = +1

sin270o = sin3p/2 = -1

xo = Vo = NBwA(1)

xo = Vo = +- NBwA

+- = shows direction of induced current

Relation b/w x and xo

x = NBwAsin(2pft)

x = xosin(2pft)

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