A motor has a back emf of 110 V and an armature current of 90 A when running at 1500 rpm. Deter

step 1 Hi, first question you have a motor has a back AMF of 110 volts and an amateur current 90 ampers

A motor has a back emf of 110 V and an armature current of...

A motor has a back emf of $110 \mathrm{~V}$ and an armature current of 90 A when running at 1500 rpm. Determine the power and the torque developed within the armature. Power $=($ Armature current $)($ Back emf $)=(90 \mathrm{~A})(110 \mathrm{~V})=9.9 \mathrm{~kW}$ From Chapter 10, power $=\tau \omega$ where $\omega=2 \pi f=2 \pi(1500 \times 1 / 60)$ $\mathrm{rad} / \mathrm{s}$ $$ \text { Torque }=\frac{\text { Power }}{\text { Angular speed }}=\frac{9900 \mathrm{~W}}{(2 \pi \times 25) \mathrm{rad} / \mathrm{s}}=63 \mathrm{~N} \cdot \mathrm{m} $$

A motor has a back emf of $110 \mathrm{~V}$ and an armature current of 90 A when running at 1500 rpm. Determine the power and the torque developed within the armature.
Power $=($ Armature current $)($ Back emf $)=(90 \mathrm{~A})(110 \mathrm{~V})=9.9 \mathrm{~kW}$
From Chapter 10, power $=\tau \omega$ where $\omega=2 \pi f=2 \pi(1500 \times 1 / 60)$ $\mathrm{rad} / \mathrm{s}$
$$
\text { Torque }=\frac{\text { Power }}{\text { Angular speed }}=\frac{9900 \mathrm{~W}}{(2 \pi \times 25) \mathrm{rad} / \mathrm{s}}=63 \mathrm{~N} \cdot \mathrm{m}
$$

Key Concepts

Back EMF

Back electromotive force (emf) is the voltage generated by a motor’s armature as it rotates within a magnetic field. This induced voltage opposes the applied voltage and is directly proportional to the motor’s speed. Understanding back emf is crucial in analyzing how electrical energy is converted into mechanical energy within a motor.

Electrical Power in Motors

Electrical power in a motor is calculated as the product of the current flowing through the armature and the effective voltage, which in this case is the back emf. This calculation indicates the rate at which electrical energy is being converted into mechanical energy, and is the starting point for further analysis of motor performance.

Torque and Angular Speed Relation

The relationship between torque, angular speed, and power is given by the equation Power = Torque × Angular Speed. This formula is essential in determining the amount of torque produced by the motor when the power output and rotational speed are known, linking the electrical input to the mechanical output.

Unit Conversion from RPM to Radians per Second

Motor speed is often provided in revolutions per minute (rpm), but many formulas in rotational dynamics require the angular speed in radians per second. The conversion is achieved using the formula ? = 2? × (rpm/60), ensuring consistency in units for accurate calculation of torque and other related quantities.

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