A shunt-connected motor delivers an output power of 24 hp at...

A shunt-connected motor delivers an output power of 24 hp at 1200 rpm while operating from a source voltage of $440 \mathrm{V}$ and drawing $I_{L}=50 \mathrm{A}$. The resistances are $R_{A}=0.05 \Omega$ and $R_{F}+R_{\text {adj }}=100 \Omega$. Find the developed torque and efficiency of the motor

Key Concepts

Torque Calculation

In rotating machinery, the relationship between power and torque is given by the equation P = T × ?, where P is the power delivered, T is the developed torque, and ? is the angular speed in radians per second. To determine torque when power and rotational speed are known, it is essential to convert the speed from revolutions per minute (rpm) to radians per second and then rearrange the equation to solve for torque.

Motor Efficiency

Motor efficiency is a measure of how effectively electrical input power is converted into mechanical output power. It is defined as the ratio of the output power to the input power, expressed as a percentage. Understanding efficiency involves an evaluation of various losses such as copper losses, core losses, and mechanical losses, which can reduce the overall performance of the motor.

DC Shunt Motor Characteristics

In a DC shunt motor, the field winding is connected in parallel with the armature. This configuration typically provides good speed regulation and relatively constant speed over a wide range of loads. The shunt connection means that the field current remains fairly constant, minimizing variations in the developed torque and contributing to stable motor performance.

Electrical Losses in Motors

Electrical losses in motors primarily include resistive (copper) losses occurring in the armature and field windings. These losses are calculated by considering the voltage drops caused by the resistances in the circuits. Accurately accounting for these losses is critical when evaluating the input power versus the actual mechanical output power, as they directly affect motor efficiency.

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