# Derive EMF Equation of DC Generator

## Derive EMF Equation of DC Generator

In the DC Generator when a conductor (Armature winding) rotates in magnetic field, it cuts the magnetic lines of force and emf is induced in the conductor ( Armature Winding) according to Faraday’s law of electromagnetic induction. The magnitude of induced emf depends on number of conductors, magnetic field strength and speed of the coil.

Let \\\;\\φ = Flux per pole in Weber.\\Z = Total Number of armature conductors. \\N = Speed of armature (rpm).\\P = Number of Poles.\\A = Number of parallel paths. \\Eg = Emf induced in parallel path or Emf Generated.

According to Faraday’s law of Electromagnetic induction.\\\;\\ Average emf generated in one conductor = \frac{Total\;flux\;cut}{time\;taken}=\frac{dφ }{dt}\\\;\\

Total Flux = Pφ\\Total Flux cut per Conductors in one revolution,dφ = Pφ\\Number of revolutions per minute = N\\Number of revolutions per second = \frac{N}{60}\\ Time taken to complete one revolution,dt = \frac{60}{N}

Emf generated per conductor = \frac{dφ}{dt}=\frac{P\phi }{\frac{60}{N}}\\\;\\Emf generated per conductor =\frac{PφN}{60}

Total Number of Conductors = Z\\Total Number of Parallel paths = A\\\;\\Number of Conductors per parallel path = \frac{Z}{A}

Total Emf generated or Total Emf Induced per parallel path = Emf generated per conductor \times Number of conductors per parallel path\\\;\\Total Emf generated or Total Emf Induced per parallel path = \frac{P\phi N}{60}\times\frac{Z}{A}\\\;\\Total Emf generated or Total Emf Induced per parallel path = \frac{P\phi NZ}{60A}\\A = 2 \timesplex (for Wave Winding)\\A = P\timesplex (For Lap Winding)