Question
Download Solution PDFA 220 V, 7 HP series motor is mechanically coupled to a fan and draws 25 A and runs at 300 rpm when connected to a 220 V with no external resistance. The torque required by the fan is proportional to the square of the speed. Ra = 0.6 Ω and Rse = 0.4 Ω. Determine the power delivered to the fan. (Assume 1 hp = 746 W)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Problem Statement: A 220 V, 7 HP series motor is mechanically coupled to a fan and draws 25 A and runs at 300 rpm when connected to a 220 V supply with no external resistance. The torque required by the fan is proportional to the square of the speed. The motor resistances are given as Ra = 0.6 Ω and Rse = 0.4 Ω. We need to determine the power delivered to the fan. (Assume 1 HP = 746 W).
Solution:
Step 1: Understanding the given data:
- Rated Voltage, V = 220 V
- Current, I = 25 A
- Speed, N = 300 rpm
- Torque required by the fan is proportional to the square of the speed (T ∝ N²).
- Armature resistance, Ra = 0.6 Ω
- Series field resistance, Rse = 0.4 Ω
- Total resistance (Rtotal) = Ra + Rse = 0.6 Ω + 0.4 Ω = 1 Ω
- 1 HP = 746 W
Step 2: Calculate the back EMF (Eb):
The back EMF (Eb) in a series motor can be calculated as:
Eb = V - I × Rtotal
Substitute the given values:
Eb = 220 - (25 × 1)
Eb = 220 - 25 = 195 V
Step 3: Calculate the power delivered to the fan:
The mechanical power developed by the motor is given by:
Pmech = Eb × I
Substitute the values of Eb and I:
Pmech = 195 × 25 = 4875 W
Convert this power to HP:
Pmech (in HP) = Pmech (in W) ÷ 746
Pmech (in HP) = 4875 ÷ 746 ≈ 6.54 HP
Step 4: Verify the proportionality of torque and speed:
Since the torque required by the fan is proportional to the square of the speed (T ∝ N²), the mechanical power delivered to the fan must align with this torque-speed relationship. The calculated power of 6.54 HP is consistent with the given operating conditions of the motor and fan system.
Conclusion:
The power delivered to the fan is 6.54 HP.
Correct Option: Option 1
Additional Information
To further understand the analysis, let’s evaluate the other options:
Option 2: 36 HP
This value is significantly higher than the calculated power of 6.54 HP. Such a high power output is not possible given the motor’s operating conditions and the current drawn by it. This option is incorrect.
Option 3: 4880 HP
This is an unrealistic value for the power delivered by a 7 HP motor. The motor is mechanically coupled to a fan, and the calculated power output (6.54 HP) is within the expected range. This option is incorrect.
Option 4: 0.15 HP
This value is far too low compared to the calculated power output of 6.54 HP. It does not match the motor’s operating conditions or the current drawn by it. This option is incorrect.
Conclusion:
Based on the analysis, the correct answer is Option 1: 6.54 HP. The other options are either unrealistic or do not match the given data and conditions.
Last updated on Jul 15, 2025
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