A transformer has a core loss of 100 W at 3/4th full load. Its full load copper loss when maximum efficiency occurs at full load is:

Explanation:

Transformer Loss Analysis

Definition: Transformers are electrical devices used to transfer electrical energy between circuits through electromagnetic induction. Two primary types of losses occur in a transformer during operation: core losses (also called iron losses) and copper losses. Core losses are constant and depend on the supply voltage and frequency, while copper losses depend on the load current.

Core Loss: Core loss, also known as iron loss, arises due to hysteresis and eddy currents in the transformer’s core material. These losses remain constant regardless of the load conditions and are determined by the supply voltage and frequency.

Copper Loss: Copper loss occurs due to the resistance of the transformer windings when current flows through them. Copper losses are proportional to the square of the load current and vary with the load.

Efficiency of Transformers: The efficiency of a transformer is the ratio of the output power to the input power. Maximum efficiency occurs when core loss equals copper loss.

Given Data:

• Core loss = 100 W (at 3/4th full load)
• Maximum efficiency occurs at full load.

Solution:

To determine the full load copper loss, we use the concept that maximum efficiency occurs when:

Core Loss = Copper Loss

Since the transformer operates at maximum efficiency at full load, the copper loss at full load must equal the core loss. Thus:

Copper Loss at Full Load = Core Loss

Copper Loss = 100 W

This gives the correct answer as Option 2: 100 W.

Additional Information

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

Option 1: 75 W

This option suggests that the copper loss at full load is 75 W, which would mean the transformer operates at maximum efficiency when the copper loss is less than the core loss. This is incorrect because maximum efficiency occurs when copper loss equals core loss.

Option 3: 133.34 W

This option assumes a copper loss higher than the core loss, which would result in reduced efficiency rather than maximum efficiency. The condition for maximum efficiency, as stated, is that core loss equals copper loss, making this option incorrect.

Option 4: 177.78 W

Similar to option 3, this option suggests a copper loss significantly higher than the core loss. This violates the condition for maximum efficiency and is thus incorrect.

Conclusion:

In transformer efficiency analysis, understanding the relationship between core loss and copper loss is crucial. At maximum efficiency, these two losses are equal. Therefore, in this scenario, the full load copper loss is equal to the constant core loss of 100 W, making Option 2 the correct answer. The other options fail to satisfy the condition for maximum efficiency and are thus incorrect.