Back emf is 85.9 V.
Explanation:
Given-
Resistance, R = 3.75Ω
Current, I = 9.1 A
Supply Voltage, V = 120 V
Back emf = ?
Assumption - There is no effects of inductance.
A motor will have a back emf that opposes the supply voltage, as the motor speeds up the back emf increases and has the effect that the difference between the supply voltage and the back emf is what causes the current to flow through the armature resistance.
So if 9.1 A flows through the resistance of 3.75Ω then by Ohms law,
The voltage across the resistance would be
v = I x R
= 9.1 x 3.75
= 34.125 volts
We know,
supply voltage = back emf + voltage across the resistance
By plugging in the values,
120 V = back emf + 34.125 V
Back emf = 120 - 34.125
= 85.9 Volts
Therefore, back emf is 85.9 V.
