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Q. Derive the expression for generated emf in a dc generator.
Ans.
Expression for Generated emf in a DC Generator
We shall now derive an expression for the emf generated in a d.c. generator.
Let Φ = flux/pole in Wb
Z = total no. of armature conductors
P = no. of poles
A = no. of parallel paths = 2......for wave winding
= P....for lap winding
N = speed of armature in r.p.m.
Eg = e.m.f. of the generator = e.m.f./parallel path
Flux cut by one conductor in one revolution of the armature, dΦ = pΦ webers
Time taken to complete one revolution,
dt = 60/n sec.
e.m.f. generated/conductor dΦ/dt = PΦ/60/N = PΦN/60 volts
e.m.f. generator, Eg = e.m.f. per parallel path
= (e.m.f/conductor) × No. of conductor in series per parallel path
= PΦN/60 × Z/A
Eg = PΦZN/60A
A = Z...for wave winding
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