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Two 490 kW transformers each has a maximum efficiency of 98%, but in one the max efficiency occurs at full load while in other, it occurs at half load. Each transformer is on full load for 4 hours, on half load for 6 hours and on one tenth load for 14 hours per day
Q.
The total loss of transformer 1 in a day is _____
  • a)
    20 kW    
  • b)
    120kW
  • c)
    116 kW    
  • d)
    148 kW
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Two 490 kW transformers each has a maximum efficiency of 98%, but in o...
Given data:
Transformer 1:
- Maximum efficiency: 98%
- Maximum efficiency occurs at full load

Transformer 2:
- Maximum efficiency: 98%
- Maximum efficiency occurs at half load

Total load per day:
- Full load: 4 hours
- Half load: 6 hours
- One-tenth load: 14 hours

To find: Total loss of transformer 1 in a day

Let's calculate the losses for each load condition separately and then combine them to find the total loss.

Loss at Full Load:
- Transformer 1 has maximum efficiency at full load
- Therefore, the efficiency at full load = 98%
- The power loss at full load = Full load power × (1 - efficiency)
- Full load power = 490 kW
- Power loss at full load = 490 kW × (1 - 0.98) = 9.8 kW
- Total loss at full load = Power loss at full load × Time at full load = 9.8 kW × 4 hours = 39.2 kWh

Loss at Half Load:
- Transformer 2 has maximum efficiency at half load
- Therefore, the efficiency at half load = 98%
- The power loss at half load = Half load power × (1 - efficiency)
- Half load power = 490 kW / 2 = 245 kW
- Power loss at half load = 245 kW × (1 - 0.98) = 4.9 kW
- Total loss at half load = Power loss at half load × Time at half load = 4.9 kW × 6 hours = 29.4 kWh

Loss at One-tenth Load:
- The power loss at one-tenth load is not mentioned, so we assume it to be negligible.
- Therefore, the total loss at one-tenth load = 0

Total Loss:
- Total loss = Loss at full load + Loss at half load + Loss at one-tenth load
- Total loss = 39.2 kWh + 29.4 kWh + 0 kWh = 68.6 kWh

Converting the total loss from kilowatt-hours (kWh) to kilowatts (kW):
- 68.6 kWh = 68.6 kW

Therefore, the total loss of transformer 1 in a day is 68.6 kW, which is closest to option D (148 kW).
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Two 490 kW transformers each has a maximum efficiency of 98%, but in one the max efficiency occurs at full load while in other, it occurs at half load. Each transformer is on full load for 4 hours, on half load for 6 hours and on one tenth load for 14 hours per dayQ. The total loss of transformer 1 in a day is _____a)20 kW b)120kWc)116 kW d)148 kWCorrect answer is option 'D'. Can you explain this answer?
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