How is the specific electric loading related to copper losses and temperature rise?

The specific electric loading (also known as the current density) in electrical machines such as transformers and electric motors is a critical factor influencing both the copper losses and the temperature rise within the machine. Let’s explore how it relates to each of these factors:

1. Relation to Copper Losses:

Copper losses, also known as I²R losses or resistive losses, occur in the windings of electrical machines due to the resistance of the copper (or sometimes aluminum) conductors. The specific electric loading is a measure of the electric current per unit length of the circumference of the armature (in the case of rotating machines) or per unit cross-sectional area of the core (in transformers).

The formula for copper losses is (P_{cu} = I^2R), where (I) is the electric current and (R) is the resistance of the winding. Since specific electric loading directly influences the amount of current flowing through the windings, higher specific electric loadings lead to higher currents for a given resistance, thereby increasing the copper losses due to the (I^2R) relationship. Essentially, as specific electric loading increases, copper losses increase non-linearly due to the square term of the current in the loss equation.

2. Relation to Temperature Rise:

The temperature rise in electrical machines is a result of several factors, including the aforementioned copper losses, as well as core losses, friction, and windage losses, among others. The temperature