Running at 1200 rpm from a 280- V source, a scrics-connected...

Running at 1200 rpm from a $280-$ V source, a scrics-connected de motor draws an armature current of 25 A. The ficld resistance is $0.2 \Omega,$ and the armature resistance is $0.3 \Omega$ Assuming that the flux is proportional to the field current, determine the speed at which the armature current is 10 A.

Key Concepts

Resistive Voltage Drops in Motor Circuits

The resistive voltage drops across the motor’s armature and field windings play a crucial role in the overall voltage distribution in the circuit. When the operating current changes, these resistive losses change proportionally, which in turn affects the voltage available for generating back EMF, and ultimately influences the motor’s speed under varying load conditions.

DC Motor Voltage and Back EMF Equation

In DC motors, the applied voltage is split into the voltage drop across the motor’s resistances (armature and field or series resistance) and the back electromotive force (back EMF). The voltage equation V = E_b + I(R_a + R_f) encapsulates this balance, where E_b is the back EMF, I is the current, and R_a and R_f are the armature and field resistances respectively.

Back EMF, Speed, and Flux Relationship

The back EMF (E_b) in a DC motor is directly proportional to both the magnetic flux (?) and the rotational speed (?) of the motor, typically expressed as E_b = k??. This relationship allows one to analyze how changes in speed or flux affect the motor’s voltage balance, ensuring that for a given applied voltage, variations in current (and therefore flux) will necessitate adjustments in speed to maintain equilibrium.

Field Flux in Series Motors

In series-connected DC motors, the field winding is connected in series with the armature, meaning the field current is the same as the armature current. Consequently, the magnetic flux is proportional to the current. This makes the motor’s performance highly dependent on the current, as any change in current affects the flux and thereby the back EMF and speed.

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