A circular armature coil is used in a motor with a uniform magnetic field of 2.6

Question

A circular armature coil is used in a motor with a uniform magnetic field of 2.65 T. The coil has a diameter 85 cm, a resistance of 50 ?, and generates a back emf of 94 VRMS when running a full speed under no load at the angular frequency ?A.
(A) At what angular frequency, ?B relative to ?A does the coil be need to be rotated to generate a back emf of 74VRMS?

(B) If this motor is operating on 120 VRMS now with a load (e.g running a fan) and at the angular frequency ?A, how much current is flowing throught the motor?

Explanation / Answer

a)

Induced EMF

E=NBAW

so

EA/EB =WA/WB

=>WB =(EB/EA) *WA

WB =(74/94)*WA

WB =0.7872*WA

so answer is 0.7872

b)

I=V-E/R =120-94/50

I=0.52 A

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