Derive EMF Equation of DC Generator

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)

Read Also

  1. Armature Winding | What is armature winding
  2. Construction of DC Generator
  3. Simple Loop Generator
About AJAZ UL HAQ 136 Articles
AJAZ UL HAQ is an Assistant Electrical Engineer and has 10.5 Years of Experience in operation & maintenance, erection, Design of Transmission and Distribution Electrical System, Internal Electrification of Buildings, Electrical Substations. He has worked on Projects - Integrated Power development Scheme (IPDS), Prime Minister's Development Package (PMDP) and Re-structured Accelerated Power Development and Reforms Programme (RAPDRP).