Transformer sizing: What kVA rating is required if the transformer must deliver up to 8 A at a secondary voltage of 2 kV?

Introduction / Context:
Selecting a transformer requires estimating apparent power in volt-amperes. The kVA rating must meet or exceed the product of the maximum secondary voltage and current because transformers are rated in apparent power rather than real power due to varying power factor loads.

Given Data / Assumptions:

• I_max = 8 A (secondary).
• V_secondary = 2 kV = 2000 V.
• Ideal transformer assumptions; rating is based on apparent power S = V * I.

Concept / Approach:
Apparent power S (VA) = V * I. Convert to kVA by dividing by 1000. This is independent of power factor for the purpose of transformer nameplate rating.

Step-by-Step Solution:
S = V * I = 2000 * 8S = 16,000 VAS = 16 kVA

Verification / Alternative check:
Quick check: 2 kV * 10 A would be 20 kVA, thus 8 A gives 16 kVA. The proportional reasoning matches the exact calculation.

Why Other Options Are Wrong:

• 8 kVA or 4 kVA: Underrated; risk of overloading at full current.
• 0.25 kVA: Two orders of magnitude too small.

Common Pitfalls:
Confusing kW with kVA, or forgetting to convert kilovolts and kilovolt-amperes properly. Always compute apparent power for transformer sizing.

Final Answer:
16 kVA