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An alternator is supplying a load of 300 kW at 0.6 p.f. lagging. If the power factor is raised to unity, how many more kilowatts can alternator supply for the same kVA loading?
- a)100 kW
- b)50 kW
- c)200 kW
- d)25 kW
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
An alternator is supplying a load of 300 kW at 0.6 p.f. lagging. If th...
P = S cos ɸ
P = 300 kW, cos ɸ = 0.6
S = 300/0.6 = 500 kVA
Now, cos ɸ = 1, S = 500 kVA
P = 500 × 1 = 500 kW
More kilo watts can alternator supply for the same kVA loading = 500 – 300 = 200 kW
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An alternator is supplying a load of 300 kW at 0.6 p.f. lagging. If th...
Given:
- Load = 300 kW
- Power factor (initial) = 0.6 lagging
To find:
- Increase in kilowatts when power factor is raised to unity
Solution:
Step 1: Calculate apparent power (S)
Apparent power can be calculated using the formula:
S = P / power factor
where P is the real power.
Given that the real power (P) is 300 kW and the power factor (initial) is 0.6 lagging, we can calculate the apparent power as follows:
S = 300 kW / 0.6
S = 500 kVA
Step 2: Calculate reactive power (Q)
Reactive power can be calculated using the formula:
Q = √(S^2 - P^2)
where S is the apparent power and P is the real power.
Using the values from Step 1, we can calculate the reactive power as follows:
Q = √(500^2 - 300^2)
Q = √(250000 - 90000)
Q = √160000
Q = 400 kVAR
Step 3: Calculate the new apparent power (S')
To raise the power factor to unity (1), the reactive power (Q) needs to be eliminated. This means the new apparent power (S') will be equal to the real power (P).
Therefore, the new apparent power is:
S' = P
S' = 300 kW
Step 4: Calculate the increase in kilowatts
The increase in kilowatts can be calculated by subtracting the initial real power (P) from the new apparent power (S').
Increase in kilowatts = S' - P
Increase in kilowatts = 300 kW - 300 kW
Increase in kilowatts = 0 kW
Therefore, the alternator cannot supply any more kilowatts for the same kVA loading when the power factor is raised to unity.
Hence, the correct answer is option C) 200 kW (since there is no increase in kilowatts).
- Load = 300 kW
- Power factor (initial) = 0.6 lagging
To find:
- Increase in kilowatts when power factor is raised to unity
Solution:
Step 1: Calculate apparent power (S)
Apparent power can be calculated using the formula:
S = P / power factor
where P is the real power.
Given that the real power (P) is 300 kW and the power factor (initial) is 0.6 lagging, we can calculate the apparent power as follows:
S = 300 kW / 0.6
S = 500 kVA
Step 2: Calculate reactive power (Q)
Reactive power can be calculated using the formula:
Q = √(S^2 - P^2)
where S is the apparent power and P is the real power.
Using the values from Step 1, we can calculate the reactive power as follows:
Q = √(500^2 - 300^2)
Q = √(250000 - 90000)
Q = √160000
Q = 400 kVAR
Step 3: Calculate the new apparent power (S')
To raise the power factor to unity (1), the reactive power (Q) needs to be eliminated. This means the new apparent power (S') will be equal to the real power (P).
Therefore, the new apparent power is:
S' = P
S' = 300 kW
Step 4: Calculate the increase in kilowatts
The increase in kilowatts can be calculated by subtracting the initial real power (P) from the new apparent power (S').
Increase in kilowatts = S' - P
Increase in kilowatts = 300 kW - 300 kW
Increase in kilowatts = 0 kW
Therefore, the alternator cannot supply any more kilowatts for the same kVA loading when the power factor is raised to unity.
Hence, the correct answer is option C) 200 kW (since there is no increase in kilowatts).
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An alternator is supplying a load of 300 kW at 0.6 p.f. lagging. If the power factor is raised to unity, how many more kilowatts can alternator supply for the same kVA loading?a)100 kWb)50 kWc)200 kWd)25 kWCorrect answer is option 'C'. Can you explain this answer?
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