A circular armature coil is used in a motor with a uniform magnetic field of 3.1

Question

A circular armature coil is used in a motor with a uniform magnetic field of 3.15 T. The coil has a diameter 70 cm, a resistance of 45 ?, and generates a back emf of 104 VRMSwhen running a full speed under no load at the angular frequency ?A.
(A) At what angular frequency, ?B relative to ?A does the coil need to be rotated to generate a back emf of 84 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 through the motor?

  A

Explanation / Answer

ANSWER:

On part A you'll just want to take the rotated emf value (smaller Vrms) and divide it by the given back emf of the coil at full speed under no load at ?A (larger Vrms).

SO, 84/104

0.7307

for PART B

On part B just take the 120 Vrms and subtract the ?A emf value at full speed under no load and then divide by the resistance.

so, (120-104)/70

0.2285

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