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A squirrel cage type induction motor when started by means of a Y/Δ starter takes 150% of full load line current and develops 45% of full load torque at starting. If an auto transformer is employed with 75% tapping, the starting torque developed by the motor is ____
  • a)
    0.56 Tf 
  • b)
    0.76 Tf 
  • c)
    2.25 Tf    
  • d)
    0.45 Tf 
Correct answer is option 'B'. Can you explain this answer?
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A squirrel cage type induction motor when started by means of a Y/[...


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A squirrel cage type induction motor when started by means of a Y/[...
Given data:

- Starting current (I start) = 150% of full load current (I FL)
- Starting torque (T start) = 45% of full load torque (T FL)
- Auto transformer tapping = 75%

To find: Starting torque developed by the motor with the auto transformer.

Solution:

1. Calculation of starting current and starting torque:

- Starting current (I start) = 150% of full load current (I FL)
- Starting torque (T start) = 45% of full load torque (T FL)

2. Calculation of reduced voltage:

- An auto transformer with 75% tapping implies that the voltage applied to the motor will be 75% of the rated voltage.
- Therefore, the reduced voltage (V start) = 0.75 × rated voltage (V rated)

3. Calculation of starting current with auto transformer:

- The starting current with the auto transformer can be calculated using the formula:
I start(auto) = (V rated / V start) × I start
- Substituting the given values, we get:
I start(auto) = (V rated / 0.75V rated) × 1.5I FL
I start(auto) = 2I FL

4. Calculation of starting torque with auto transformer:

- The starting torque with the auto transformer can be calculated using the formula:
T start(auto) = (V start / V rated)^2 × T start
- Substituting the given values, we get:
T start(auto) = (0.75V rated / V rated)^2 × 0.45T FL
T start(auto) = 0.76T FL

Therefore, the starting torque developed by the motor with the auto transformer is 0.76 times the full load torque. Hence, the correct option is (B) 0.76 TFL.
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A squirrel cage type induction motor when started by means of a Y/Δ starter takes 150% of full load line current and develops 45% of full load torque at starting. If an auto transformer is employed with 75% tapping, the starting torque developed by the motor is ____a)0.56 Tfb)0.76 Tfc)2.25 Tf d)0.45 TfCorrect answer is option 'B'. Can you explain this answer?
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