At its normal operating speed, an electric fan motor draws only 10.9% of the current it draws when it just begins to turn the fan blade. The fan is plugged into a 120.0-V socket. What back emf does the motor generate at its normal operating speed?

Answer 1

The current when it "just begins to turn the blade" is a starting surge current. There is no back emf (Vb) at that time. Let R be the resistance of the motor coils.

The starting surge current is 120V/R.
The current at normal operating speed is (120 - Vb)/R

(120 - Vb)/R = 0.109*(120/R)

Vb = 120 - 13.08 = 106.9 V