# 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.

## 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: 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: As the machine is spinning at ‘N’ rpm (radials per minute), the time taken for one revolution is given by: Therefore the EMF induced per conductor is given by: The total EMF induced in the machine, if there are ‘Z’ number of conductors and ‘A’ number of parallel paths is: The above is the EMF equation of DC machines.