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A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).
Correct answer is '125.29'. Can you explain this answer?
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Verified Answer
A cylindrical rotor synchronous generator with constant real power out...
At Pconstant, Ia1 cos φ1 = Ia2 cos φ2
cos φ1 = 0.9
tan φ1 = 0.484 = Q/P
⇒ 2Q/P = 0.9686 = tan φ2
cos φ2 = 0.7182
∴ 100 × 0.9 = Ia2 × 0.7182
⇒ Ia2 = 125.29 A
cos φ1 = 0.9
tan φ1 = 0.484 = Q/P
⇒ 2Q/P = 0.9686 = tan φ2
cos φ2 = 0.7182
∴ 100 × 0.9 = Ia2 × 0.7182
⇒ Ia2 = 125.29 A
Most Upvoted Answer
A cylindrical rotor synchronous generator with constant real power out...
Given:
- Cylindrical rotor synchronous generator
- Constant real power output
- Constant terminal voltage
- Supplying 100 A current to a 0.9 lagging power factor load
To find:
- Armature current after connecting an ideal reactor in parallel with the load
Solution:
Step 1: Calculate the initial reactive power:
The initial power factor of the load is 0.9 lagging, which means the load has a reactive power requirement.
We know that the power factor (PF) is defined as the ratio of real power (P) to apparent power (S), and it can be calculated as:
PF = P / S
Given that the load is operating at 0.9 lagging power factor and the real power output of the generator is constant, we can write:
0.9 = P / S
Since the real power output is constant, the apparent power (S) is also constant. Therefore, the reactive power (Q) can be calculated using the Pythagorean theorem:
S^2 = P^2 + Q^2
Substituting the given values:
S^2 = P^2 + (0.9S)^2
Simplifying the equation:
S^2 = P^2 + 0.81S^2
0.19S^2 = P^2
Q^2 = 0.19S^2 - P^2
Taking the square root of both sides:
Q = √(0.19S^2 - P^2)
Step 2: Calculate the new reactive power:
Given that the total lagging reactive power requirement of the load is twice the previous value, the new reactive power requirement (Q') can be calculated as:
Q' = 2Q = 2√(0.19S^2 - P^2)
Step 3: Calculate the new armature current:
The new armature current can be calculated using the new reactive power requirement and the power factor of the load.
We know that the power factor (PF') is defined as the ratio of real power (P) to apparent power (S'), and it can be calculated as:
PF' = P / S'
Since the real power output is constant, the apparent power (S') can be calculated using the Pythagorean theorem:
S'^2 = P^2 + (Q')^2
Simplifying the equation:
S'^2 = P^2 + (2√(0.19S^2 - P^2))^2
S'^2 = P^2 + 4(0.19S^2 - P^2)
S'^2 = P^2 + 0.76S^2 - 4P^2
S'^2 = -3P^2 + 0.76S^2
S'^2 = -3P^2 + 0.76(S^2 - P^2)
S'^2 = -3P^2 + 0.76S^2 - 0.76P^2
S'^2 = 0.24S^2 - 4.76P^2
Simplifying further:
S'^2 - 0.24S^2 = - 4.76P^
- Cylindrical rotor synchronous generator
- Constant real power output
- Constant terminal voltage
- Supplying 100 A current to a 0.9 lagging power factor load
To find:
- Armature current after connecting an ideal reactor in parallel with the load
Solution:
Step 1: Calculate the initial reactive power:
The initial power factor of the load is 0.9 lagging, which means the load has a reactive power requirement.
We know that the power factor (PF) is defined as the ratio of real power (P) to apparent power (S), and it can be calculated as:
PF = P / S
Given that the load is operating at 0.9 lagging power factor and the real power output of the generator is constant, we can write:
0.9 = P / S
Since the real power output is constant, the apparent power (S) is also constant. Therefore, the reactive power (Q) can be calculated using the Pythagorean theorem:
S^2 = P^2 + Q^2
Substituting the given values:
S^2 = P^2 + (0.9S)^2
Simplifying the equation:
S^2 = P^2 + 0.81S^2
0.19S^2 = P^2
Q^2 = 0.19S^2 - P^2
Taking the square root of both sides:
Q = √(0.19S^2 - P^2)
Step 2: Calculate the new reactive power:
Given that the total lagging reactive power requirement of the load is twice the previous value, the new reactive power requirement (Q') can be calculated as:
Q' = 2Q = 2√(0.19S^2 - P^2)
Step 3: Calculate the new armature current:
The new armature current can be calculated using the new reactive power requirement and the power factor of the load.
We know that the power factor (PF') is defined as the ratio of real power (P) to apparent power (S'), and it can be calculated as:
PF' = P / S'
Since the real power output is constant, the apparent power (S') can be calculated using the Pythagorean theorem:
S'^2 = P^2 + (Q')^2
Simplifying the equation:
S'^2 = P^2 + (2√(0.19S^2 - P^2))^2
S'^2 = P^2 + 4(0.19S^2 - P^2)
S'^2 = P^2 + 0.76S^2 - 4P^2
S'^2 = -3P^2 + 0.76S^2
S'^2 = -3P^2 + 0.76(S^2 - P^2)
S'^2 = -3P^2 + 0.76S^2 - 0.76P^2
S'^2 = 0.24S^2 - 4.76P^2
Simplifying further:
S'^2 - 0.24S^2 = - 4.76P^
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A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer?
Question Description
A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer?.
A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylindrical rotor synchronous generator with constant real power output and constant terminal voltage is supplying 100 A current to a 0.9 lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the total lagging reactive power requirement of the load is twice the previous value while the real power remains unchanged. The armature current is now _______ A (rounded off to 2 decimal places).Correct answer is '125.29'. Can you explain this answer?.
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