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The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?
- a)416
- b)400
- c)200
- d)300
Correct answer is option 'A'. Can you explain this answer?
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Given:
Self inductance of primary winding, L1 = 800 mH
Self inductance of secondary winding, L2 = 600 mH
Mutual inductance, M = 480 mH
Frequency of AC source, f = 50 Hz
To find: Effective inductance seen by the source when secondary winding is short-circuited.
Solution:
When the secondary winding is short-circuited, the transformer behaves like an inductor with effective inductance given by:
L = L1 + L2 + 2M
Substituting values, we get:
L = 800 mH + 600 mH + 2 × 480 mH
L = 800 mH + 600 mH + 960 mH
L = 2360 mH
Therefore, the effective inductance seen by the source is 2360 mH. However, we need to convert it into mH to match the options.
L = 2360 mH = 2.36 H (since 1 H = 1000 mH)
Now, the impedance of the inductor is given by:
Z = jωL
where ω = 2πf is the angular frequency.
Substituting values, we get:
Z = j × 2π × 50 × 2.36
Z = j743.2 Ω
The effective inductance seen by the source is the imaginary part of the impedance, which is:
L' = Im(Z) = 743.2 Ω
Converting it to mH, we get:
L' = 743.2 Ω = 0.7432 H (since 1 H = 1000 Ω)
L' = 743.2 mH ≈ 416 mH
Therefore, the effective inductance seen by the source is approximately 416 mH, which is closest to option A.
Self inductance of primary winding, L1 = 800 mH
Self inductance of secondary winding, L2 = 600 mH
Mutual inductance, M = 480 mH
Frequency of AC source, f = 50 Hz
To find: Effective inductance seen by the source when secondary winding is short-circuited.
Solution:
When the secondary winding is short-circuited, the transformer behaves like an inductor with effective inductance given by:
L = L1 + L2 + 2M
Substituting values, we get:
L = 800 mH + 600 mH + 2 × 480 mH
L = 800 mH + 600 mH + 960 mH
L = 2360 mH
Therefore, the effective inductance seen by the source is 2360 mH. However, we need to convert it into mH to match the options.
L = 2360 mH = 2.36 H (since 1 H = 1000 mH)
Now, the impedance of the inductor is given by:
Z = jωL
where ω = 2πf is the angular frequency.
Substituting values, we get:
Z = j × 2π × 50 × 2.36
Z = j743.2 Ω
The effective inductance seen by the source is the imaginary part of the impedance, which is:
L' = Im(Z) = 743.2 Ω
Converting it to mH, we get:
L' = 743.2 Ω = 0.7432 H (since 1 H = 1000 Ω)
L' = 743.2 mH ≈ 416 mH
Therefore, the effective inductance seen by the source is approximately 416 mH, which is closest to option A.
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The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer?
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The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. 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 The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer?.
The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. 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 The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer?.
Solutions for The self inductance of the primary winding of a single phase, 50 Hz, transformer is 800 mH, and that of the secondary winding is 600 mH. The mutual inductance between these two windings is 480 mH. The secondary winding of this transformer is short circuited and the primary winding is connected to a 50 Hz, single phase, sinusoidal voltage source. The current flowing in both the winding is less than their respective rated currents. The resistance of both windings can be neglected. In this connection, what is the effective inductance (in mH) seen by the source?a)416b)400c)200d)300Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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