# EMF equation of a DC Generator

An emf is induced in a DC generator, when a conductor is rotated in a magnetic field. The emf induced in a conductor depends on the speed of rotation of the conductor and the flux produced from a field winding.

Let us drive the equation of an emf induced in a DC generator. Before deriving the equation, learn about the construction and working principle of DC generator.

Let P = number of poles.

Z = total number of conductor in the armature.

A = number of parallel paths, into which the conductors are grouped. So each parallel path will have Z/A conductor in series.

N = speed of the rotor in revolution per minute(rpm)

N/60 = Speed of the rotor in revolutions per second.

Time taken by the rotor to complete one revolution, dt = 1/(N/60)= 60/N second

In one revolution of the rotor, the total flux Φ cut the by each conductor in the stator poles, dΦ = ΦP weber

By faraday’s law of electromagnetic induction, the emf induced is proportional to rate of change of flux.

Since there are *Z/A *conductor in series in each parallel path, the emf induced is given by

The above equation represents the general equation for emf induced in a DC generator. The armature conductors in a DC generator can be connected in two ways. They are lap winding and wave winding.

For lap wound machines, the number of parallel paths is equal to the number of poles(A = P).

For such machine, the emf equation is given by,

In wave wound machine, the number of parallel paths is equal to 2(A = 2).

The emf equation of a wave wound machine is given by,

**If a DC generator has 8 poles and the flux produced is 0.025 weber. The generator has 450 conductors in the armature and rotates at 1500 rpm, **

the EMF generated by the Lap wounded DC generator is

the EMF generated by the wave wounded generator is

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