Answer :
The maximum efficiency of a 100 kVA single-phase transformer with 600 W full-load copper loss and 500 W iron loss occurs at approximately 91.3 kVA, which is when the variable copper loss equals the constant iron loss. Option c is the answer.
The question pertains to determining the maximum efficiency load point of a transformer with known full-load copper and iron losses. To find the maximum efficiency point, we need to consider when the variable copper loss equals the constant iron loss. The copper loss varies with the square of the load, so we set the full-load copper loss equal to the iron loss, and calculate the load at which this equality holds. This is done by taking the square root of the ratio of iron loss to full-load copper loss, and then multiplying that value by the full-load kVA rating of the transformer.
We have the formula: Efficiency = (Output Power) / (Output Power + Losses). The losses are comprised of copper losses, which change with the load, and iron (or core) losses, which remain constant regardless of the load. Maximum efficiency arises where copper losses equal iron losses. Thus, the formula for finding the load at which maximum efficiency occurs is:
Load (kVA) at max efficiency = Rated kVA
cdot √(Iron loss / Full-load copper loss).
Given the values, the calculation is as follows:
Load (kVA) at max efficiency = 100 kVA
cdot √(500 W / 600 W) = 100 kVA
cdot √(5/6)
≈ 91.3 kVA.
As such, the maximum efficiency occurs when the transformer is loaded to approximately 91.3 kVA.
