A certain shunt-connected de motor has RA=4 Ωand VT=240 V . At a speed of 1000 rpm, the induced

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A certain shunt-connected de motor has RA=4 Ωand VT=240 V ....

A certain shunt-connected de motor has $R_{A}=4 \Omega$ and $V_{T}=240 \mathrm{V} .$ At a speed of $1000 \mathrm{rpm},$ the induced armature voltage is $120 \mathrm{V}$. Plot the torque-speed characteristic $\left(T_{\text {cev }} \text { versus } n_{m}\right)$ to scale.

Key Concepts

DC Shunt Motor

A DC shunt motor is one in which the field windings are connected in parallel (or 'shunt') with the armature, resulting in a nearly constant field flux when operated from a constant voltage source. This configuration provides good speed regulation and a relatively constant speed under varying loads, making it useful for applications requiring steady rotational speed.

Armature Circuit Equation

The armature circuit can be described by the equation VT = E + I_A × R_A, where VT is the terminal voltage, E is the induced or back electromotive force, I_A is the armature current, and R_A is the armature resistance. This equation is fundamental to understanding the relationship between applied voltage, back EMF, and the current that contributes to torque production.

Back EMF

Back electromotive force (EMF) is the voltage induced in the armature windings as the motor rotates in the magnetic field, and it is directly proportional to the speed of the motor. As motor speed increases, the back EMF increases, which in turn reduces the effective voltage across the armature resistance and thus the armature current, influencing the motor’s torque output.

Torque-Speed Characteristics

The torque-speed characteristic of a DC motor shows how the motor’s output torque varies with its rotational speed. For a shunt motor, as the speed increases, the back EMF increases and consequently the armature current (and thus torque) decreases. Plotting this curve involves understanding that maximum torque occurs at lower speeds when the back EMF is lower, and as the motor speeds up, the available torque decreases in a largely linear fashion under constant voltage conditions.

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