Answer:

The kVAR rating of the shunt capacitor required for a particular kW rating of an induction motor is more for a lower rated speed motor. This is because the kVAR rating of the capacitor is directly related to the reactive power (kVAR) required by the motor.

Reactive Power and Power Factor:
When an induction motor operates, it requires both active power (kW) to perform useful work and reactive power (kVAR) to establish the magnetic field in the motor. The ratio of the active power to the apparent power (kVA) is known as the power factor (PF). A lower power factor indicates a higher requirement of reactive power.

Effect of Speed on Reactive Power:
The speed of an induction motor is directly related to the frequency of the power supply. In a lower rated speed motor, the frequency is lower, resulting in a lower reactance of the motor windings. This lower reactance leads to a higher requirement of reactive power to establish the magnetic field.

Role of Shunt Capacitor:
A shunt capacitor is used to provide the necessary reactive power to the induction motor and improve the power factor. It compensates for the lagging reactive power of the motor and reduces the overall reactive power requirement from the power system.

Relation between Motor Speed and Shunt Capacitor Rating:
Since a lower rated speed motor requires a higher amount of reactive power, the shunt capacitor rating needs to be increased to compensate for this additional reactive power. Therefore, the kVAR rating of the shunt capacitor required is more for a lower rated speed motor.

Conclusion:
The kVAR rating of the shunt capacitor required for a particular kW rating of an induction motor is more for a lower rated speed motor. The lower frequency and reactance of the motor windings in a lower rated speed motor result in a higher requirement of reactive power, which is compensated by increasing the shunt capacitor rating.