A 300 kVA transformer has 95% efficiency at full load, 0.8 p.f. lagging and 96% efficiency at half load, unity p.f.What is the maximum efficiency (in %) at unity p.f. load? (Answer up to one decimal place)Correct answer is '96.2'. Can you explain this answer?

Question

Answer

Answer

Find the iron and copper loss first by
efficiency=(x.VA.pf) / {(x.VA.pf)+Pi +(x^2.Pcu)}. .....(1)
we'll get Pi+Pcu = 12/.95 =12.6315 ....(2)
& 4Pi +Pcu = 6/.24 = 25 ....(3)

equ 3 - 2 we get,

Pi = 4.1228 KW
& Pcu = 8.5087 KW

since, Xm=√(Pi/Pcu)
Xm = 0.696.88
~ 0.697
now
solving for equ (1)
efficiency=0 .962014
=96.2%

Answer

Transformer Efficiency

Efficiency is an important parameter to consider when evaluating the performance of a transformer. It is defined as the ratio of output power to input power, expressed as a percentage. In other words, it represents the amount of power that is successfully transferred from the primary side to the secondary side of the transformer.

Efficiency at Full Load

Given that the transformer has a rating of 300 kVA, we can assume that at full load, it delivers 300 kVA of apparent power. The efficiency at full load is given as 95%. This means that the transformer is able to successfully transfer 95% of the input power to the load, while 5% is lost as losses (primarily copper and iron losses) within the transformer itself.

Efficiency at Half Load

At half load, the transformer delivers 150 kVA of apparent power. The efficiency at this load condition is given as 96%. This indicates that the transformer is able to transfer 96% of the input power to the load, while 4% is lost as losses within the transformer.

Maximum Efficiency at Unity Power Factor Load

To find the maximum efficiency at unity power factor (p.f.) load, we need to determine the load condition at which the efficiency is maximum. At unity power factor, the power delivered to the load is equal to the apparent power.

Let's assume that the transformer delivers P watts of real power at unity power factor. Since the power factor is unity, the apparent power is also P VA.

At unity power factor, the efficiency can be calculated as follows:

Efficiency = (Real Power Out / Real Power In) x 100

Since the real power delivered to the load is P watts and the input power is also P watts, the efficiency simplifies to:

Efficiency = (P / P) x 100 = 100%

Therefore, at unity power factor, the efficiency of the transformer is always 100%. This indicates that the transformer is able to transfer all the input power to the load at unity power factor, without any losses within the transformer itself.

Conclusion

The maximum efficiency at unity power factor load is always 100%, as there are no losses within the transformer itself at this load condition. Therefore, the given answer of '96.2%' is incorrect. The correct answer is 100%.

Similar Electrical Engineering (EE) Doubts

A 500 kVA, 3-phase transformer has iron losses of 300 W and full load copper losses of 600 W. The percentage load at which the transformer is expected to have maximum efficiency is (Answer up to one decimal plac e) Correct answer is '70.7'. Can you explain this answer?

The maximum efficiency of 550 KVA, 3300/430 V, 50 Hz 1 transformer is 98% and occurs at ¾ full load, unity power factor. If the impedance is 10%, calculate the regulation (in %) at full load at 0.8 P.F lagging. Correct answer is between '7,8'. Can you explain this answer?

The maximum efficiency of a 100 kVA, signal phase transformer is 98% and occurs at 80% of full load at 0.8 P.F. If the leakage impedance of the transformer is 5%, find voltage regulation (in %) at rated load of 0.8 power factor lagging. Correct answer is '3.8'. Can you explain this answer?

Top Courses for Electrical Engineering (EE)View all

Network Theory (Electric Circuits)

GATE Electrical Engineering (EE) Mock Test Series 2025

General Aptitude for GATE

GATE Notes & Videos for Electrical Engineering

Engineering Mathematics

Top Courses for Electrical Engineering (EE)

Top Courses for Electrical Engineering (EE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company