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EMF Equation for DC Machine

EMF Equation for DC Machine

DC machine may be either works as a dc motor or dc generator. EMF equation is important for both. In case of DC generator an induced emf is called generated emf and in case of DC motors generated emf is called Back or Counter emf  The DC generator is rotate with the help of prime mover. Prime mover is directly coupled to the generator. When armature of dc generator rotates its conductor cuts by the magnetic flux that is produce in field winding and this results of an emf is induced in it. The induced emf depends upon the type of winding of dc generator whether it is wave or lap. In this article, we will drive the emf equation for dc machine.


Φ = flux per pole in weber

Z = total number of armature conductor

= number of slots * number of conductors per slot

P = number of parallel paths in armature

N = rotation speed of the armature in revolution per minute (r.p.m)

E = emf induced in any parallel path in armature

Eg = Generated emf

Flux cut by one conductor in one revolution = PΦ wb

Time to complete one revolution, t = 60/N seconds.

Average induced emf in one conductor,

emf equation for dc machine

The number of conductors connected in series in each parallel path = Z/A

The emf generated across terminals,

E = Average emf induced in one conductor * the number of conductors connected in series in each parallel path

Number of parallel paths in wave winding, A = 2

Number of parallel paths in lap winding, A = P

Conclusions from EMF Equation for DC Machine

  • In above equation, poles remain constant.
  • The emf induced in the armature is directly proportional to the flux per pole and speed.
  • The polarity of induced emf in armature is depends upon the connections of field winding and the direction of rotation. If reversed the connection of field winding and direction of rotation, the polarity induced emf will change.
  • The induced emf is fundamental phenomenon to all dc machines either it is operated as generator or motor.
  • When the machine is operating as a generator, this induced emf is called the generated emf Eg.
  • When the machine is operating as a motor, this induced emf is called back or counter emf, Eb. This emf plays an important role in dc motor. By using this equation we can find back emf.
  • Wave winding is used for high  voltage and low current applications and where as Lap winding used where large current at low voltage is generated.

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DC Generator

DC Generator

DC Generator is an electrical machine that converts mechanical energy into dc electrical energy.

It is usually driven by some source of mechanical power which may be a diesel or petrol engine, steam turbine etc.

Working Principle of Generator

The working principle of dc generator based on the dynamically induced emf. It states that whenever there is a relative movement of a conductor with respect to field, emf is induced in the conductor. In simple words, according to faraday’s law of electromagnetic induction we can say that whenever a conductor cuts across the magnetic field, an emf is induced in the conductors.

In case of dc generator, the magnetic field is stationary and the conductors move. The direction of induced emf is given by Fleming’s right hand rule.

For induced emf, the essential component of the generator is

  • Conductor or a group of conductors
  • A magnetic field
  • Motion of the conductor with respect to filed

Types of DC Generators

The magnetic field in a generator is usually produced by electromagnets. So, the generators are generally classified according to their methods of field excitation. On the basis of these criteria, they can be classified as

Separately Excited DC Generator

Self Excited DC Generator

DC generator

Separately Excited DC Generator

A dc generator in which current is supplied to the field winding from an external dc source is known as separately excited  generator. The voltage output depends upon speed and filed current. The separately excited generators are rarely used in practice because additional dc source is required for producing necessary flux.

sepsartely excited dc generator

Self Excited DC Generator

A dc generator whose field winding is supplied current from the output of the generator it self is called a self excited  generator. According to connection of field winding with armature, it is divided into three types.

  • Series wound generator
  • Shunt wound generator
  • Compound wound generator

Series Wound Generator

In series wound generator, the filed winding is connected in series with the armature winding. Therefore, full armature current of load current flows through the filed winding. Field winding has few turns of thick wire having low resistance.

series wound dc generator

Shunt Wound Generator

In a shunt wound generator, the filed winding is connected in parallel with the armature. Full terminal voltage applied across the filed winding. Field winding has many turns of fine wire having very high resistance.


shunt wound dc generator

Compound Wound Generator

In compound wound generators, two field windings are used on each pole. One winding is connected in series and other is connected in parallel with armature. The compound wound generators are divided into two types.

  • Long shunt
  • Short shunt

compound wound dc generator

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