The power input to a 3-phase induction motor is 50 kW. Total losses in the stator are 2 kW. Find the mechanical power developed if the motor is running with a slip of 5%.

Explanation:

Mechanical Power Developed in a 3-Phase Induction Motor

Problem Statement: The power input to a 3-phase induction motor is 50 kW. Total losses in the stator are 2 kW. Find the mechanical power developed if the motor is running with a slip of 5%.

Solution:

To find the mechanical power developed by the 3-phase induction motor, we need to follow these steps:

1. Calculate the Power Input to the Rotor (P_r):

The power input to the rotor can be found by subtracting the stator losses from the total power input to the motor.

Given:

• Total Power Input (P_in) = 50 kW
• Total Stator Losses (P_stator) = 2 kW

Power Input to the Rotor (P_r) = P_in - P_stator

P_r = 50 kW - 2 kW = 48 kW

2. Calculate the Rotor Copper Losses (P_copper):

Rotor copper losses are proportional to the slip of the motor. The formula to calculate rotor copper losses is:

P_copper = Slip × Power Input to the Rotor (P_r)

Given:

• Slip (s) = 5% = 0.05

P_copper = 0.05 × 48 kW = 2.4 kW

3. Calculate the Mechanical Power Developed (P_mech):

The mechanical power developed by the motor can be found by subtracting the rotor copper losses from the power input to the rotor.

P_mech = P_r - P_copper

P_mech = 48 kW - 2.4 kW = 45.6 kW

Therefore, the mechanical power developed by the motor is 45.6 kW.

Correct Option:

The correct option is:

Option 4: 45.6 kW

Additional Information:

To further understand the analysis, let’s evaluate the other options:

Option 1: 41.3 kW

This option is incorrect because it does not account for the proper calculation of rotor copper losses and mechanical power developed. The mechanical power developed is higher than this value.

Option 2: 43.5 kW

This option is also incorrect. The calculation of mechanical power developed results in a higher value than this option.

Option 3: 47.2 kW

This option is incorrect because it overestimates the mechanical power developed. The correct calculation shows that the mechanical power developed is lower than this value.

Conclusion:

Understanding the calculation of mechanical power developed in a 3-phase induction motor involves accounting for the stator losses, rotor copper losses, and the slip of the motor. By following the proper steps and formulas, we can accurately determine the mechanical power developed, which is essential for evaluating the performance and efficiency of the motor.