As the armature turns, a voltage is created in its loops. On account of a generator, the emf of the pivot is known as the Generated emf or Armature emf and is indicated as Er = Eg. On account of an engine, the emf of the pivot is known as Back emf or Counter emf and spoke to as Er = Eb. The articulation for emf is same for both the tasks. I.e., for Generator just as for Motor.
Derivation of EMF Equation of a DC Machine – Generator and Motor
Let,
- P – Number of poles of the machine
- ϕ – Flux per pole in Weber.
- Z – Total number of armature conductors.
- N – Speed of armature in revolution per minute (r.p.m).
- A – number of parallel paths in the armature winding.
In one revolution of the armature, the flux cut by one conductor is given as
Time taken to complete one revolution is given as
Therefore, the average induced e.m.f in one conductor will be
Putting the value of (t) from Equation (2) in the equation (3) we will get
The number of conductors connected in series in each parallel path = Z/A.
Therefore, the average induced e.m.f across each parallel path or the armature terminals is given by the equation shown below.
Where n is the speed in revolution per second (r.p.s) and given as
For a given machine, the number of poles and the number of conductors per parallel path (Z/A) are constant. Hence, equation (5) can be written as
Where, K is a constant and given as
Therefore, the average induced emf equation can also be written as
Where K1 is another constant and hence induced emf equation can be written as
Where ω is the angular velocity in radians/second is represented as
Along these lines, plainly the instigated emf is straightforwardly relative to the speed and motion per shaft. The extremity of instigated emf relies on the bearing of the attractive field and the heading of revolution. If both of the two is turn around the extremity changes, however, if two are switched the extremity stays unaltered.
This initiated emf is an essential wonder for all the DC Machines whether they are filling in as a generator or engine.
If the machine DC Machine is filling in as a Generator, the instigated emf is given by the condition demonstrated as follows.
Where Eg is the Generated Emf
If the machine DC Machine is working as a Motor, the induced emf is given by the equation shown below.
In a motor, the induced emf is called Back Emf (Eb) because it acts opposite to the supply voltage.
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