Calculating Three Phase Transformer Rating (kVA)

To determine the rating of a three-phase transformer, we use the formula for apparent power in a three-phase system.

The formula for the apparent power (S) of a three-phase transformer is given by:

\(S = \sqrt{3} \times V_L \times I_L\)

Where:

• \(S\) is the apparent power in Volt-Amperes (VA) or kilo-Volt-Amperes (kVA).
• \(V_L\) is the line voltage in Volts (V).
• \(I_L\) is the line current in Amperes (A).

From the question, we are given the following values:

• Load Current (\(I_L\)) = 139.1 A
• Secondary Voltage (\(V_L\)) = 415 V

Now, we can substitute these values into the formula to calculate the apparent power:

\(S = \sqrt{3} \times 415 \text{ V} \times 139.1 \text{ A}\)

We know that \(\sqrt{3} \approx 1.732\). So, the calculation becomes:

\(S \approx 1.732 \times 415 \times 139.1 \text{ VA}\)

\(S \approx 1.732 \times 57626.5 \text{ VA}\)

\(S \approx 99801.778 \text{ VA}\)

To express the rating in kVA, we divide the result by 1000:

\(S \approx \frac{99801.778}{1000} \text{ kVA}\)

\(S \approx 99.80 \text{ kVA}\)

Comparing this calculated value with the given options:

• 50 kVA
• 57.72 kVA
• 100 kVA
• 173 kVA

The calculated value of approximately 99.80 kVA is closest to 100 kVA.

Therefore, the rating of the transformer would be approximately 100 kVA.