Final answer:
The back electromotive force (back EMF) of a 120 V motor that draws 8.00 A at its normal speed and 20.0 A when first starting is 60 V.
Step-by-step explanation:
Back electromotive force (back EMF) is the voltage generated in the opposite direction to the applied voltage in a motor or generator. It is caused by the change in magnetic flux through the motor's windings. When a motor draws 8.00 A at its normal speed, it means that the current I flowing through the motor is 8.00 A. The back EMF can be calculated using the formula:
Back EMF = Applied Voltage - (Current x Resistance)
Given that the applied voltage is 120 V, and the current is 8.00 A, we can substitute these values into the formula to find the back EMF:
Back EMF = 120 V - (8.00 A x Resistance)
To find the value of the resistance, we need another equation. When the motor draws 20.0 A when first starting, we can write:
20.0 A = 120 V / (Resistance)
Solving for resistance gives us:
Resistance = 120 V / 20.0 A
Substituting this value back into the original equation for the back EMF:
Back EMF = 120 V - (8.00 A x (120 V / 20.0 A))
Simplifying the equation gives the back EMF:
Back EMF = 60 V