Question

A transformer operates most efficiently at \( \frac{3}{4} \) full-load. Its iron loss (\(P_i\)) and full-load copper loss (\(P_c\)) are related as _______.

• A. \(P_i/P_c = 4/3\)
• B. \(P_i/P_c = 16/9\)
• C. \(P_i/P_c = 3/4\)
• D. \(P_i/P_c = 9/16\)

Hint:

At max efficiency: Iron loss = copper loss at the operating load → Use square of the load fraction!

Answer 1

The Correct Option is D

Step 1: Condition for maximum efficiency in transformer.
Maximum efficiency occurs when: \[ \text{Iron loss} = \text{Copper loss at that load}. \] Step 2: Given Load.
Load = \( \frac{3}{4} \) full-load
So, copper loss at this load: \[ P_{\text{cu}} = \left( \frac{3}{4} \right)^2 P_c = \frac{9}{16} P_c \] Step 3: Apply efficiency condition.
\[ P_i = \frac{9}{16} P_c \Rightarrow \frac{P_i}{P_c} = \frac{9}{16} \] Conclusion: The ratio of iron loss to full-load copper loss is \( \boxed{\frac{9}{16}} \)