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A 500 KVA transformer has constant loss of 500W and copper losses at full load are 2000W. Then at what load, is the efficiency maximum?
- a)250KVA
- b)500KVA
- c)1000KVA
- d)125KVA
Correct answer is option 'A'. Can you explain this answer?
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A 500 KVA transformer has constant loss of 500W and copper losses at ...
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A 500 KVA transformer has constant loss of 500W and copper losses at ...
Calculation of Efficiency
To find the load at which the efficiency is maximum, we need to calculate the efficiency at different loads and then compare them. The efficiency of a transformer is given by the formula:
Efficiency = Output Power / Input Power
where Output Power = KVA x Power Factor and Input Power = Output Power + Total Losses
Given data:
KVA = 500
Constant Losses = 500 W
Copper Losses at full load = 2000 W
1. Calculation of Input Power at full load:
Output Power at full load = KVA x Power Factor = 500 x 1 = 500 kW
Total Losses at full load = Constant Losses + Copper Losses = 500 + 2000 = 2500 W
Input Power at full load = Output Power at full load + Total Losses at full load = 500000 + 2500 = 502500 W
2. Calculation of Efficiency at full load:
Efficiency at full load = Output Power at full load / Input Power at full load
= 500000 / 502500
= 0.995
3. Calculation of Input Power at half load:
Output Power at half load = KVA x Power Factor = 250 x 1 = 250 kW
Total Losses at half load = Constant Losses + Copper Losses = 500 + (0.25)^2 x 2000 = 562.5 W
Input Power at half load = Output Power at half load + Total Losses at half load = 250000 + 562.5 = 250562.5 W
4. Calculation of Efficiency at half load:
Efficiency at half load = Output Power at half load / Input Power at half load
= 250000 / 250562.5
= 0.996
5. Calculation of Input Power at one-fourth load:
Output Power at one-fourth load = KVA x Power Factor = 125 x 1 = 125 kW
Total Losses at one-fourth load = Constant Losses + Copper Losses = 500 + (0.5)^2 x 2000 = 1000 W
Input Power at one-fourth load = Output Power at one-fourth load + Total Losses at one-fourth load = 125000 + 1000 = 126000 W
6. Calculation of Efficiency at one-fourth load:
Efficiency at one-fourth load = Output Power at one-fourth load / Input Power at one-fourth load
= 125000 / 126000
= 0.992
7. Calculation of Input Power at three-fourth load:
Output Power at three-fourth load = KVA x Power Factor = 375 x 1 = 375 kW
Total Losses at three-fourth load = Constant Losses + Copper Losses = 500 + (0.75)^2 x 2000 = 1750 W
Input Power at three-fourth load = Output Power at three-fourth load + Total Losses at three-fourth load = 375000 + 1750 = 376750 W
8. Calculation of Efficiency at three-fourth load:
Efficiency at three-fourth load = Output Power at three-fourth load / Input Power at three-fourth load
= 375000 / 376750
= 0.995
Conclusion
To find the load at which the efficiency is maximum, we need to calculate the efficiency at different loads and then compare them. The efficiency of a transformer is given by the formula:
Efficiency = Output Power / Input Power
where Output Power = KVA x Power Factor and Input Power = Output Power + Total Losses
Given data:
KVA = 500
Constant Losses = 500 W
Copper Losses at full load = 2000 W
1. Calculation of Input Power at full load:
Output Power at full load = KVA x Power Factor = 500 x 1 = 500 kW
Total Losses at full load = Constant Losses + Copper Losses = 500 + 2000 = 2500 W
Input Power at full load = Output Power at full load + Total Losses at full load = 500000 + 2500 = 502500 W
2. Calculation of Efficiency at full load:
Efficiency at full load = Output Power at full load / Input Power at full load
= 500000 / 502500
= 0.995
3. Calculation of Input Power at half load:
Output Power at half load = KVA x Power Factor = 250 x 1 = 250 kW
Total Losses at half load = Constant Losses + Copper Losses = 500 + (0.25)^2 x 2000 = 562.5 W
Input Power at half load = Output Power at half load + Total Losses at half load = 250000 + 562.5 = 250562.5 W
4. Calculation of Efficiency at half load:
Efficiency at half load = Output Power at half load / Input Power at half load
= 250000 / 250562.5
= 0.996
5. Calculation of Input Power at one-fourth load:
Output Power at one-fourth load = KVA x Power Factor = 125 x 1 = 125 kW
Total Losses at one-fourth load = Constant Losses + Copper Losses = 500 + (0.5)^2 x 2000 = 1000 W
Input Power at one-fourth load = Output Power at one-fourth load + Total Losses at one-fourth load = 125000 + 1000 = 126000 W
6. Calculation of Efficiency at one-fourth load:
Efficiency at one-fourth load = Output Power at one-fourth load / Input Power at one-fourth load
= 125000 / 126000
= 0.992
7. Calculation of Input Power at three-fourth load:
Output Power at three-fourth load = KVA x Power Factor = 375 x 1 = 375 kW
Total Losses at three-fourth load = Constant Losses + Copper Losses = 500 + (0.75)^2 x 2000 = 1750 W
Input Power at three-fourth load = Output Power at three-fourth load + Total Losses at three-fourth load = 375000 + 1750 = 376750 W
8. Calculation of Efficiency at three-fourth load:
Efficiency at three-fourth load = Output Power at three-fourth load / Input Power at three-fourth load
= 375000 / 376750
= 0.995
Conclusion
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A 500 KVA transformer has constant loss of 500W and copper losses at full load are 2000W. Then at what load, is the efficiency maximum?a)250KVAb)500KVAc)1000KVAd)125KVACorrect answer is option 'A'. Can you explain this answer?
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