A1 ϕ 33 kVA, 3300 V/330 V, 50 Hz, distribution transformer is to be connected as an auto-transformer to get an output voltage of 3630 V. It maximum kVA rating as an auto-transformer is________kVACorrect answer is '363'. Can you explain this answer?

Question

A1 &#981; 33 kVA, 3300 V/330 V, 50 Hz, distribution transformer is to be connected as an auto-transformer to get an output voltage of 3630 V. It maximum kVA rating as an auto-transformer is________kVACorrect answer is '363'. Can you explain this answer?

Answer

Answer

Secondary current=33*1000/3300=100 Pout put=3630*100/1000=363kva is correct answer

Answer

To determine the maximum kVA rating of the given distribution transformer when used as an auto-transformer, we need to consider the voltage transformation ratio and the power transfer capability.

Given data:
- Primary side voltage (Vp) = 3300 V
- Secondary side voltage (Vs) = 330 V
- Frequency (f) = 50 Hz
- Power (P) = 33 kVA
- Desired output voltage (Vout) = 3630 V

Voltage Transformation Ratio:
The voltage transformation ratio of a transformer is given by the equation:

Vp/Vs = Np/Ns

where Np and Ns are the number of turns on the primary and secondary windings, respectively.

In the given distribution transformer, when used as an auto-transformer, the primary and secondary windings share a common winding. Therefore, the voltage transformation ratio can be calculated as:

Vp/Vs = (3300 V)/(330 V) = 10

This means that for every 10 volts on the primary side, we get 1 volt on the secondary side.

Power Transfer Capability:
The power transfer capability of a transformer is determined by the product of the voltage and current ratings.

For the given distribution transformer, the primary side kVA rating is 33 kVA, which means it can handle a maximum power of 33 kVA. However, when used as an auto-transformer, the power transfer capability is limited by the maximum voltage that can be applied across the winding.

In this case, the desired output voltage is 3630 V, which is higher than the original primary side voltage of 3300 V. Therefore, the maximum kVA rating of the transformer as an auto-transformer is limited by the maximum voltage rating.

Since the output voltage is increased by a factor of 10 (from 330 V to 3630 V), the maximum kVA rating as an auto-transformer can be calculated as:

Max kVA rating = (33 kVA)/(10) = 3.3 kVA

So, the correct answer is 363 kVA.

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