Core losses in a transformer are proportional to:

Core Losses in a Transformer

Definition: Core losses (also known as iron losses) in a transformer are the losses that occur in the magnetic core of the transformer. These losses are primarily caused by two phenomena: hysteresis loss and eddy current loss. Core losses are independent of the load and depend solely on the supply voltage and frequency.

Working Principle:

The magnetic core of a transformer is subjected to alternating magnetic flux due to the alternating current in the primary winding. This alternating flux causes two types of losses in the core:

• Hysteresis Loss: This loss is caused by the repeated magnetization and demagnetization of the core material as the magnetic field alternates. The energy lost in this process depends on the hysteresis loop area of the core material, the volume of the core, and the frequency of the magnetic flux.
• Eddy Current Loss: This loss is caused by circulating currents induced in the core material due to the changing magnetic flux. These currents flow in closed loops within the core and generate heat, leading to energy loss. Eddy current loss depends on the square of the frequency and the square of the magnetic flux density.

Mathematical Representation:

The total core loss (P_core) in a transformer can be expressed as the sum of hysteresis loss (P_h) and eddy current loss (P_e):

P_core = P_h + P_e

The hysteresis loss is proportional to the frequency (f), while the eddy current loss is proportional to the square of the frequency (f²). Thus, the total core loss is strongly dependent on the frequency.

Correct Option Analysis:

The correct option is:

Option 1: The square of the frequency.

Core losses in a transformer are proportional to the square of the frequency because of the dominance of eddy current loss, which varies directly with f². Although hysteresis loss is proportional to frequency (f), the overall dependence of core loss on frequency is heavily influenced by the f² relationship of eddy current loss. This makes option 1 the most accurate answer.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 2: The square of the stator current.

This option is incorrect. Core losses are independent of the load, and hence they are not influenced by the stator current. Stator current affects copper losses (I²R losses) in the winding rather than core losses.

Option 3: The square of the voltage.

While core losses are dependent on the supply voltage, they are not directly proportional to the square of the voltage. Instead, core losses are primarily influenced by the frequency of the alternating magnetic flux, as explained earlier.

Option 4: The square of the load current.

This option is also incorrect. Core losses are independent of the load current. Load current affects copper losses in the transformer windings but does not impact the core losses, which are constant and dependent on the supply voltage and frequency.

Conclusion:

Core losses in a transformer are a crucial factor in determining its efficiency and performance. These losses are caused by hysteresis and eddy currents in the core, and their dependence on frequency makes it essential to carefully select the operating frequency of the transformer. Among the given options, option 1 is correct because core losses are proportional to the square of the frequency, primarily due to the contribution of eddy current loss.