A transformer has core loss = 500 W and full-load copper loss = 500 W.1.Maximum efficiency occurs at full load condition.2.At half load, copper loss becomes 125 W.3.Efficiency at half load is lower than full load efficiency.4.Condition for maximum efficiency is that copper loss equals core loss.Which of the above statements is/are correct?

Correct Answer: B - 1, 2, 3 and 4

Quick Concept Explanation

At x p.u. load, transformer output is proportional to x while copper loss is proportional to x² and iron loss remains approximately constant. The given losses make the maximum-efficiency load x=sqrt(500/500)=1 p.u. Every statement follows numerically, so B is correct. Key relation: Pcu(x)=x²Pcu,FL. Here Pcu(0.5)=0.25×500=125 W. Maximum η: x²Pcu,FL=Pi → x=1.

Exam focus: If core loss equals full-load copper loss, maximum efficiency is at full load—an instant result. Common trap: Scaling copper loss linearly with load instead of with load squared.

Statement-wise Verification

• Statement 1 - Correct.
  Maximum efficiency occurs at full load condition.
  Maximum efficiency occurs when Pcu=Pi; this equality is given at full load.
• Statement 2 - Correct.
  At half load, copper loss becomes 125 W.
  Copper loss scales with current/load squared, so at 0.5 load it is 0.5²×500=125 W.
• Statement 3 - Correct.
  Efficiency at half load is lower than full load efficiency.
  Full load is the maximum-efficiency operating point in this case, so moving to half load gives lower efficiency (for the same power factor assumption).
• Statement 4 - Correct.
  Condition for maximum efficiency is that copper loss equals core loss.
  If core loss equals full-load copper loss, maximum efficiency is at full load—an instant result.

Core Concept

At x p.u. load, transformer output is proportional to x while copper loss is proportional to x² and iron loss remains approximately constant. The efficiency curve therefore has a peak when the two loss components are equal.

Formula / Key Relationship

Pcu(x)=x²Pcu,FL. Here Pcu(0.5)=0.25×500=125 W. Maximum η: x²Pcu,FL=Pi → x=1.

Step-by-Step Check

The given losses make the maximum-efficiency load x=sqrt(500/500)=1 p.u. Every statement follows numerically, so B is correct.

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 4. Option C is incorrect because it omits correct statement(s) 1, 4. Option D is incorrect because it omits correct statement(s) 3.

Answer-Key Verification Note

The uploaded provisional key marks D . After independent technical verification, the defensible answer is B . This discrepancy is stated explicitly rather than silently copying the provisional key.

Exam Shortcut / Approach

If core loss equals full-load copper loss, maximum efficiency is at full load—an instant result.

Common Mistake

Scaling copper loss linearly with load instead of with load squared.

Quick Revision

Load for Maximum Efficiency is linked with Transformer Efficiency, Transformers and Electrical Machines. If core loss equals full-load copper loss, maximum efficiency is at full load—an instant result.