A circular armature coil is used in a motor with a uniform magnetic field of 4.5

Question

A circular armature coil is used in a motor with a uniform magnetic field of 4.50 T. The coil has a diameter 85 cm, a resistance of 45 , and generates a back emf of 109 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 89 VRMS?

B = ??? A

(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?

(A)

Explanation / Answer

Here,

magnetic field , B = 4.5 T

diamtere , d = 85/2 cm

d = 42.5 cm = 0.425 m

R = 45 Ohm

Vrms = 109 Vrms

A)

Vrmsb = 89 V

as VrmsA/VrmsB = wA/wB

120/89 = wA/wB

wA/wB = 1.348

wB = 0.742 * wA

B)

as Vrms = 120 V

R = 45 Ohm

current in the motor = (120 - back emf)/R

current in the motor = (120 - 109)/45

current in the motor = 11/45

current in the motor = 0.244 A

the current in the motor is 0.244 A

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