The terms (W_{cu}), (W_s), and (W_c) are commonly used to denote different types of losses in the context of electrical transformers and similar devices. Here is a brief explanation of each type of loss and their relationship:

1. (W_{cu}) (Copper Losses):

   • Copper losses, also known as (I^2 R) losses, occur due to the resistance ((R)) in the winding conductors of the transformer. When current (I) flows through the windings, it causes heat generation, which is considered a loss. The formula for copper loss is given by (P_{cu} = I^2 R).

2. (W_s) (Stray Losses or Iron Losses):

   • Stray losses, often referred to as iron losses, include hysteresis and eddy current losses that occur in the core of the transformer. These losses depend on the magnetic properties of the core material and the frequency of the alternating current. They can be represented as:
     • Hysteresis loss: Proportional to the frequency (f) and the volume of the core.
     • Eddy current loss: Proportional to the square of the frequency and inversely proportional to the resistivity of the core material.

3. (W_c) (Core Losses):

   • Core losses are also essentially iron losses, which include both hysteresis and eddy current losses. Sometimes, the term (W_s) might specifically refer to additional stray losses not included in the standard core loss calculation.

In general, the total loss (W_t) in a transformer can be summed up as: [ W_t = W_{cu} + W_c ] or, [ W_t = W_{cu} + W_s ] depending on the context of how the losses are grouped or defined.

Practical Example and Application:

For example, if a transformer operates under loaded conditions, the total loss will be a combination of copper losses due to the windings and core losses due to the magnetic core. Accurately accounting for these losses is crucial for designing efficient transformers and predicting their performance under various operating conditions.

Summary Image for Visual Understanding:

To help visualize these losses, here is an illustrative image that breaks down the different types of losses in a transformer (assuming these images were among the relevant ones):

For further academic references and a detailed breakdown of these losses, you could explore the resources like transformer engineering textbooks or whitepapers on electrical losses in transformers.

For more specific or academic sources, consider reviewing detailed electrical engineering texts or articles that delve into transformer losses and their calculations. If you need more detailed references, please let me know!