Final answer:
The torque produced by the DC motor is 4.974 Nm. The back e.m.f of a DC motor is an electromotive force generated in the opposite direction to the applied voltage when the motor is spinning. The back e.m.f is at its maximum when the motor is spinning at its maximum speed.
Step-by-step explanation:
To calculate the torque produced by the DC motor, we need to know the power and the speed of the motor. The formula to calculate torque is:
Torque = Power / (2 * π * Speed)
Given that the power is 5 kW and the speed is 9000 rpm, we can plug these values into the formula:
Torque = 5000 W / (2 * 3.1416 * 9000/60) = 4.974 Nm (to three significant figures).
The term 'back e.m.f' of a DC motor refers to the electromotive force that is generated in the opposite direction to the applied voltage when the motor is spinning. It is caused by the motion of the conductor through the magnetic field of the motor. The back e.m.f helps to limit the current flowing through the motor and maintain a more or less constant speed.
The 'back e.m.f' of a DC motor is at its maximum when the motor is spinning at its maximum speed. At maximum speed, the back e.m.f is equal to the supply voltage, and the current flowing through the motor is minimized, allowing the motor to maintain a constant speed and operate at maximum efficiency.