Exam Question

### (a) Effects of Running an Induction Motor on Reduced Voltage
Running an induction motor on a voltage significantly lower than its rated voltage can have several detrimental effects on its performance, efficiency, and longevity. These effects stem primarily from the fundamental electromagnetic principles governing the motor's operation, particularly the relationship between voltage, magnetic flux, and current.
* **Reduced Magnetic Flux Density:** The magnetic flux ($\Phi$) within the motor's air gap is directly proportional to the applied voltage (V) and inversely proportional to the frequency (f), i.e., $$ \Phi \propto V/f $$. A reduction in voltage directly leads to a decrease in the magnetic flux density. This reduced flux is the primary cause of many subsequent issues.
* **Decreased Torque Production:** The torque developed by an induction motor is approximately proportional to the square of the applied voltage, i.e., $$ T \propto V^2 $$. Therefore, a small reduction in voltage can lead to a significant drop in both starting torque and maximum (pull-out) torque. For instance, a 10% reduction in voltage (to 90% of rated) results in a torque reduction to approximately (0.9)^2 = 0.81, or 81% of the rated torque. This can prevent the motor from starting a loaded machine or cause it to stall if the load torque exceeds the reduced maximum torque.