For a single phase transformer, the maximum efficiency occurs at 75% of the load, then \(\rm \frac{iron \ loss \ at\ full \ load }{copper \ loss \ at\ full \ load}=?\)
Transformer Efficiency and Losses
The efficiency of a transformer is maximum when the iron loss is equal to the copper loss at the specific load where maximum efficiency occurs.
Let:
- \(P_i\) be the iron loss (core loss) of the transformer. Iron loss is typically considered constant regardless of the load.
- \(P_{cu, full \ load}\) be the copper loss of the transformer at full load. Copper loss varies with the square of the load current.
- \(x\) be the fraction of full load at which the transformer is operating.
The copper loss at a load \(x\) is given by \(P_{cu, x} = x^2 \times P_{cu, full \ load}\).
Maximum Efficiency Condition
Maximum efficiency for a transformer occurs when:
\( \text{Iron Loss} = \text{Copper Loss at that load} \)
\( P_i = P_{cu, x} \)
Calculating Loss Ratio at 75% Load
We are given that the maximum efficiency occurs at 75% of the load. This means \(x = 75\% = \frac{75}{100} = \frac{3}{4}\).
Applying the maximum efficiency condition at this load level:
\( P_i = P_{cu, at \ 75\% \ load} \)
\( P_i = \left(\frac{3}{4}\right)^2 \times P_{cu, full \ load} \)
\( P_i = \frac{9}{16} \times P_{cu, full \ load} \)
Finding the Required Ratio
The question asks for the ratio of iron loss at full load to copper loss at full load, which is \(\frac{P_i}{P_{cu, full \ load}}\).
From our calculation based on the maximum efficiency condition:
\( \frac{P_i}{P_{cu, full \ load}} = \frac{9}{16} \)
This ratio tells us how the constant iron loss compares to the copper loss specifically when the transformer is operating at full load, given that maximum efficiency was observed at 75% load.
Important Questions from Transformer Copper Losses
What is the condition at which a transformer gives maximum efficiency?
- Which of the following losses remains variable during normal operation of transformer?
In a single-phase transformer, the ratio of transformation is 2 and the secondary resistance is 0.24 Ω. Find the resistance of secondary in terms of primary.
A single-phase \(400\;V,\;50\;Hz\) transformer has an iron loss of \(5000\;W\) at the rated condition. When operated at \(200\;V,\;25\;Hz\), the iron loss is \(2000\;W\). When operated at \(416\;V,\;52\;Hz\), the value of the hysteresis loss divided by the eddy current loss is ______.
The full load copper loss and iron loss of a transformer are 6400 W and 5000 W respectively the copper loss and iron loss at half load will be respectively.
