A motor has an armature resistance of 3.75 Ω. Part A If it draws 9.10 A when running at full speed and connected to a 120-V line, how large is the back emf?

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.