What factor does the additional copper losses depend upon?

The additional copper losses in electrical machines (such as transformers, motors, and generators) depend primarily on the following factors:

1. Load Current: Copper losses are proportional to the square of the load current (I^2). As the current flowing through the copper windings increases, the losses due to the resistance of the copper (I^2R losses) also increase.

2. Winding Resistance: The intrinsic resistance of the copper winding directly impacts the losses. Higher resistance leads to higher losses for the same amount of current. The resistance itself can vary with temperature; generally, as temperature increases, resistance increases, leading to higher losses.

3. Stray Load Losses: These are additional losses that increase with load and are due to various factors such as leakage flux inducing eddy currents in conductive components (not directly part of the primary circuit). These losses can be influenced by the design of the machine and the quality of materials used.

4. Frequency of Operation: In alternating current (AC) applications, higher frequencies can increase skin effect and proximity effect in conductors, effectively increasing the resistance experienced by alternating currents and thus increasing losses.

5. Temperature: The temperature of the copper winding affects its resistivity. Generally, as temperature increases, resistivity increases, leading to higher copper losses. This is why proper cooling or thermal management is critical in electrical machines to maintain efficiency.

6. Quality of Materials: The purity and type of copper used for windings can also influence copper losses. Higher