Transformer questions punish you for forgetting which side you are standing on
The arithmetic is a ratio. The mistakes are almost all bookkeeping about which winding the number belongs to.
On this page
What a transformer actually conserves
Power, near enough. Volt-amperes in equals volt-amperes out, minus losses that exam questions almost always ignore.
So if voltage goes up, current goes down in proportion. That single sentence generates every ratio you need and it means you never have to remember a formula with subscripts in it.
Write down the kVA once. It is the same number on both sides. Everything else follows from dividing it by the voltage on whichever side you want.
The three-phase factor, and when it appears
On a single-phase transformer, current is the volt-amperes divided by the voltage.
On a three-phase transformer, the same division happens but with the square root of three in the denominator alongside the voltage.
That factor is the single most common place points are lost here. It belongs in three-phase calculations and nowhere else, and questions are written so that omitting it produces a number in a plausible range.
Sizing the conductors on each side
Primary and secondary conductors are sized from their own side currents. They are not the same size and they are not sized from the same number.
Work out the current on the side you are being asked about, then size the conductor for that current the way you would any other: base ampacity, corrections, termination limit.
A question that hands you a kVA rating and both voltages is usually checking whether you compute the right side before you start looking up wire.
Overcurrent protection has its own rules
This is where transformers stop being simple ratios. Transformer overcurrent protection is not sized like ordinary conductor protection, and the permitted percentages depend on the transformer voltage rating and on whether there is protection on both sides or only one.
Read Article 450 in your own book for the table that applies. The structure of it, primary only versus primary and secondary, is what decides which row you are in.
Note also that protecting the transformer and protecting the conductors are two different obligations. Passing the transformer rules does not automatically satisfy the conductor rules.
Secondary conductors are a known trap
Transformer secondary conductors are generally not considered protected by the primary overcurrent device, except in specific configurations.
The code says this directly in Article 240 (NEC 240.4(F)). Single-phase other than two-wire, and multiphase other than delta-delta three-wire, do not get that protection.
So a candidate who assumes the primary breaker covers everything downstream has skipped a requirement, and the question was almost certainly built around that assumption.
The method
- Write the kVA down. It is the same on both sides.
- Identify which side the question is asking about.
- Divide by that side voltage, including the square root of three if it is three-phase.
- Size conductors for that side from the resulting current.
- Size transformer protection from Article 450, checking whether you have protection on one side or both.
- Check whether the secondary conductors need their own protection.
Label your two currents primary and secondary before you do anything else. Almost every wrong answer here is the right arithmetic applied to the wrong side.
What this page cites
- NEC 450.5 Overcurrent protection for transformers, by voltage rating and configuration. This was 450.3 through the 2023 edition. In 2026 450.3 is Reconditioned Equipment and both of its subsections are reserved.
- NEC 240.4(F) Transformer secondary conductors are generally not protected by the primary device. The exceptions are a single-phase transformer with a two-wire secondary and a delta-delta transformer with a three-wire secondary, which the section expressly permits the primary device to protect.
- NEC 110.14(C) The termination limit applied when sizing either side.