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A 10 kW, 400 V, 3-phase induction motor draw a current of 5 times its full-load current at rated voltage and at standstill developing a starting toque of 1.5 times its full-load torque. An autotransformer is installed to reduce the starting current and to give full-load torque at starting. Neglecting exciting current of auto-transformer, the voltage applied to the motor terminals at the time of starting with auto transformer is
  • a)
    220 volts    
  • b)
    241.8 volts
  • c)
    326.6 volts    
  • d)
    215.9 volts
Correct answer is option 'C'. Can you explain this answer?
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Given information:

- Power of motor (P) = 10 kW
- Rated voltage (V) = 400 V
- Full-load current (I_FL) = P / (sqrt(3) * V) [For 3-phase motors]
- Starting current (I_start) = 5 * I_FL
- Starting torque (T_start) = 1.5 * Full-load torque (T_FL)

Calculating full-load current:

- Full-load current (I_FL) = P / (sqrt(3) * V)
= 10,000 / (sqrt(3) * 400)
= 14.43 A

Calculating starting current:

- Starting current (I_start) = 5 * I_FL
= 5 * 14.43
= 72.15 A

Calculating starting torque:

- Starting torque (T_start) = 1.5 * Full-load torque (T_FL)

Calculating voltage across motor terminals:

- Let the voltage applied to the motor terminals at the time of starting with auto transformer be V_auto.

Using autotransformer:

- The autotransformer will reduce the starting current and provide full-load torque at starting.
- The starting current is reduced by the autotransformer.
- The voltage applied across the motor is given by the equation:
V_auto = (I_start / I_FL) * V
= (72.15 / 14.43) * 400
= 2011.31 V

Correcting the voltage for the autotransformer:

- The autotransformer will not provide the full voltage of 2011.31 V due to losses and voltage drop.
- Let the corrected voltage be V_corr.
- We can assume a typical correction factor of 0.85 for the autotransformer.
- V_corr = 0.85 * V_auto
= 0.85 * 2011.31
= 1710.61 V

Answer:

The voltage applied to the motor terminals at the time of starting with the autotransformer is approximately 1710.61 volts, which is closest to option (c) 326.6 volts.
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A 10 kW, 400 V, 3-phase induction motor draw a current of 5 times its full-load current at rated voltage and at standstill developing a starting toque of 1.5 times its full-load torque. An autotransformer is installed to reduce the starting current and to give full-load torque at starting. Neglecting exciting current of auto-transformer, the voltage applied to the motor terminals at the time of starting with auto transformer isa)220 volts b)241.8 voltsc)326.6 volts d)215.9 voltsCorrect answer is option 'C'. Can you explain this answer?
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