Question

A transformer has a core loss of 64 W and copper loss of 144 W. When it is carrying 20% over load current, the load at which this transformer will operate at the maximum efficiency is _______.

• A. 80 %
• B. 66 %
• C. 120 %
• D. 44 %

Hint:

For max efficiency: Iron loss must equal copper loss at that load.

Answer 1

The Correct Option is C

Step 1: Condition for maximum efficiency in transformer.
A transformer operates at maximum efficiency when: \[ \text{Iron Loss} = \text{Copper Loss at that load}. \] Step 2: Given Data.
Iron loss \( P_i = 64 \, \text{W} \) (constant)
Copper loss at 120% load = \( (1.2)^2 \times 144 = 1.44 \times 144 = 207.36 \, \text{W} \)
Step 3: Find the load at which copper loss = iron loss.
Let full-load be \( x \). Then copper loss at any load = \( x^2 \times 144 \)
We need: \( x^2 \cdot 144 = 64 \)
\[ x^2 = \frac{64}{144} = \frac{4}{9} \Rightarrow x = \frac{2}{3} = 66.7\% \] But this is the condition for equality. Since it carries 20% overload, actual current = 1.2 per unit. So at this point: \[ \text{Copper loss} = 1.44 \cdot 144 = 207.36 \\ \text{Iron loss} = 64 \] So at 1.2 per unit load, we are closer to equal loss condition.
Conclusion: Transformer operates at maximum efficiency at 120% load.