Electrical Engineering XYZ MCQs

Maximum efficiency will occur, when copper loss is _________ iron loss:

- Less than
- Equal to
- Greater than
- Any of the above

Correct answer: 2. Equal to

**Explanation:**

In electrical transformers, there are two primary types of losses: copper losses and iron losses. Copper losses (also known as winding losses) occur due to the resistance in the transformer’s windings through which the current flows. These losses are proportional to the square of the current flowing through the windings. Iron losses (or core losses), on the other hand, occur in the transformer’s core and are due to eddy currents and hysteresis in the core material. These losses are generally considered to be constant at a particular voltage and frequency.

The maximum efficiency in a transformer occurs when the copper losses are equal to the iron losses. This is derived from the following reasoning:

**Total Losses**: The total losses in a transformer are the sum of copper losses and iron losses. These can be represented as 𝑃_{𝑡𝑜𝑡𝑎𝑙}=𝑃_{𝑐𝑜𝑝𝑝𝑒𝑟}+𝑃_{𝑖𝑟𝑜𝑛}**Efficiency**: The efficiency of a transformer is defined as the ratio of the output power to the input power. Since losses reduce the output power from the ideal (input) power, minimizing these losses maximizes efficiency.**Condition for Maximum Efficiency**: Mathematical analysis shows that the efficiency of a transformer is maximized when the variable loss (copper loss, which changes with load) is equal to the constant loss (iron loss). The formula for copper losses can be given as 𝑃_{𝑐𝑜𝑝𝑝𝑒𝑟}=𝐼^{2}×𝑅 where 𝐼 is the load current and 𝑅 is the resistance of the windings. Since copper losses vary with the square of the current, they change with varying loads, while iron losses remain fairly constant over normal operating ranges.**Design and Practical Implications**: Transformers are often designed such that at their typical load (which might be their full-load or a fraction of it depending on the application), the copper losses equal the iron losses, thereby achieving maximum efficiency under these typical operating conditions.

Therefore, stating that maximum efficiency occurs when copper loss is equal to iron loss is an essential design and operational principle in transformer efficiency optimization.