EMF equation of DC machines

EMF equation of DC machines is a mathematical expression to calculate the EMF induced in a DC machine. As you know, the amount of EMF induced in a conductor depends on the number of turns of the coil and the rate of change of flux.

EMF equation of DC machines

Derivation of EMF equation of DC machines

Consider a motor that has ‘P’ number of poles and a ‘Z’ number of conductors per pole spinning at a speed of ‘N’ radials per second.

If ‘φ’ is the flux produced in ‘webers’, according to Faraday’s law, the EMF induced per conductor is given by:

    \[ E_{av} \propto \frac{d \phi}{dt}  \]

The above equation states that the induced EMF is directly proportional to the change in flux. The flux generated by a DC is constant. The total flux generated by all the poles is given by:

    \[ d \phi = \phi \times P  \]

As the machine is spinning at ‘N’ rpm (radials per minute), the time taken for one revolution is given by:

    \[ dt =\frac{60}{N} \]

Therefore the EMF induced per conductor is given by:

    \[ E_{av} = \frac{\phi \times P }{\frac{60}{N}} = \frac{PN \phi}{60} \]

The total EMF induced in the machine, if there are ‘Z’ number of conductors and ‘A’ number of parallel paths is:

    \[ E = \frac{PN \phi}{60} \times  \frac{Z}{A} =  \frac{PN \phi Z}{60.A} \]

The above is the EMF equation of DC machines.

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