**Finding the Rotor Copper Losses**

To calculate the rotor copper losses, we need to consider the power output and the rotation losses of the motor. The power output of the motor is given as 30 kW, and the rotation losses are stated as 1.4 kW.

The rotor copper losses can be calculated using the equation:

Rotor Copper Losses = Power Output - Rotation Losses

Substituting the given values, we have:

Rotor Copper Losses = 30 kW - 1.4 kW = 28.6 kW

Therefore, the rotor copper losses of the induction motor are 28.6 kW.

**Calculating the Operating Efficiency of the Motor**

To calculate the operating efficiency of the motor, we need to consider the power input and the power output of the motor. We are given the stator copper losses, which are 3.4 kW. However, we need to neglect any other losses for this calculation.

The power input to the motor can be calculated using the equation:

Power Input = Power Output + Stator Copper Losses

Substituting the given values, we have:

Power Input = 30 kW + 3.4 kW = 33.4 kW

The operating efficiency of the motor can be calculated using the equation:

Operating Efficiency = (Power Output / Power Input) * 100

Substituting the values, we have:

Operating Efficiency = (30 kW / 33.4 kW) * 100 = 89.82%

Therefore, the operating efficiency of the motor is approximately 89.82%.

**Explanation of the Calculation**

The rotor copper losses represent the energy lost due to the resistance of the rotor windings. These losses occur as the current flows through the rotor windings, resulting in heat dissipation.

The operating efficiency of the motor is a measure of how effectively the motor converts the input power into useful output power. It is calculated by comparing the power output to the power input. In this case, we neglect any losses other than the stator copper losses.

By calculating the rotor copper losses and the operating efficiency, we can assess the performance of the induction motor and determine the amount of energy lost during operation.