A dc motor with its rotor and field coils connected in...

A dc motor with its rotor and field coils connected in series has an internal resistance of $4.0 \Omega$. When the motor is running at full load on a $230 \mathrm{~V}$ supply, the emf in the rotor is $200 \mathrm{~V}$. (a) What is the current drawn by the motor from the supply? (b) What is the power delivered to the motor? (c) What is the mechanical power developed by the motor?

Key Concepts

DC Motor Operation

DC motors convert electrical energy into mechanical energy using the force generated by the interaction of magnetic fields and current-carrying conductors. The motor's armature, when current flows through it, generates a magnetic field that interacts with the field provided by either permanent magnets or electromagnets, resulting in torque and rotational motion.

Series Motor Characteristics

In a series DC motor, the field windings are connected in series with the armature so that the same current flows through both. This configuration affects the motor's speed-torque characteristics, making it particularly suitable for applications requiring high starting torque, though it may lead to variations in field strength with load changes.

Back Electromotive Force (EMF)

Back EMF is the voltage induced in the motor’s armature as it rotates within the magnetic field, which opposes the applied supply voltage. It plays a crucial role in regulating the current drawn by the motor and determines the effective voltage available for overcoming resistive drops within the motor’s circuitry.

Ohm's Law Application

Ohm's Law relates voltage, current, and resistance in an electrical circuit. In the context of DC motors, it is used to determine the current flowing through the internal resistance of the motor by considering the net voltage drop across that resistance, after accounting for the back EMF.

Electrical and Mechanical Power Calculations

Power in electrical machines is assessed both in terms of electrical power input and mechanical power output. Electrical power is calculated by multiplying the supply voltage by the current drawn, while mechanical power is determined by considering the voltage drop that contributes to mechanical work (i.e., the difference between the supply voltage and back EMF) multiplied by the current. These calculations help in understanding machine efficiency and performance under load.

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