A separately excited dc shunt motor is operated at constant...

A separately excited dc shunt motor is operated at constant terminal voltage and constant developed power. Assuming the armature resistance is zero, if the field current (and therefore $\left.K_a \phi\right)$ is decreased, will the speed of the machine increase or decrease, and why?

Key Concepts

DC Motor Voltage Equation

In a DC motor, the applied voltage is largely balanced by the back electromotive force (EMF) produced by the motor, following the equation V = E_back + IaRa. When armature resistance is assumed to be zero, this simplifies to V = E_back, meaning that the back EMF essentially matches the terminal voltage. This concept is fundamental because it sets the stage for understanding how speed, flux, and voltage interact in the motor.

Back Electromotive Force (EMF)

Back EMF is generated by the rotating armature in the magnetic field and is given by the product of a constant, the magnetic flux (phi), and the angular speed (omega), i.e., E_back = k * phi * omega. With a fixed terminal voltage, if the magnetic flux decreases, the motor must increase its speed to maintain the same back EMF. This inverse relation is key to understanding motor behavior when flux varies.

Magnetic Flux and Field Current

The magnetic flux in a DC motor is directly related to the field current, especially in a separately excited configuration where the field circuit is independent of the armature. A decrease in field current lowers the flux, which in turn affects torque production and the back EMF. Since the back EMF depends on both flux and speed, a reduced flux forces an increase in speed to compensate, assuming other conditions remain constant.

Developed Power and Torque-Speed Relationship

Developed power in a motor is the product of torque and speed. When operating at constant developed power, any changes in flux (and consequently torque) will influence the speed. In this scenario, with a decreased flux, the motor compensates by increasing speed to maintain the constant power output. This relationship highlights the interplay between mechanical power, electromagnetic parameters, and motor speed.

Transcript

Please give Ace some feedback