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Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X?
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Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel plan...
Solution:
Given data:
Turns of coil X, N1 = 12000
Turns of coil Y, N2 = 15000
Flux linkage between the coils, k = 45%
Current in coil X, I1 = 5A, Flux produced = Φ1 = 0.05Wb
Current in coil Y, I2 = 5A, Flux produced = Φ2 = 0.075Wb
To find:
Mutual inductance, M
Percentage of flux produced by coil Y and linking with coil X
Formula:
Mutual inductance is given by M = k√(L1L2), where L1 and L2 are the self-inductances of coils X and Y respectively.
The self-inductance of a coil is given by L = (N^2μA)/l, where N is the number of turns, μ is the permeability of the medium, A is the area of the coil, and l is the length of the coil.
Percentage of flux produced by coil Y and linking with coil X is given by (kN2/N1) × 100%.
Calculation:
Self-inductance of coil X, L1 = (N1^2μA)/l
Self-inductance of coil Y, L2 = (N2^2μA)/l
Mutual inductance, M = k√(L1L2)
Substituting the given values, we get:
L1 = (12000^2 × 4π × 10^-7 × A)/l
L2 = (15000^2 × 4π × 10^-7 × A)/l
M = 0.45√(L1L2)
We can calculate the area of the coil using the given data:
Flux produced by coil X, Φ1 = L1I1
0.05 = (12000^2 × 4π × 10^-7 × A)/l × 5
Area of coil X, A = Φ1l/(12000^2 × 4π × 10^-7 × 5)
Similarly, we can calculate the area of coil Y:
Flux produced by coil Y, Φ2 = L2I2
0.075 = (15000^2 × 4π × 10^-7 × A)/l × 5
Area of coil Y, A = Φ2l/(15000^2 × 4π × 10^-7 × 5)
Now we can substitute the values of L1, L2, A, and k in the formula for mutual inductance:
M = 0.45√((12000^2 × 4π × 10^-7 × Φ1l/(12000^2 × 4π × 10^-7 × 5)) × (15000^2 × 4π × 10^-7 × Φ2l/(15000^2 × 4π × 10^-7 × 5)))
M = 0.45√(Φ1Φ2 × l^2/(4π × 10^-7 × 25))
M = 0.45(l/10^3)√(Φ1Φ2)
M
Given data:
Turns of coil X, N1 = 12000
Turns of coil Y, N2 = 15000
Flux linkage between the coils, k = 45%
Current in coil X, I1 = 5A, Flux produced = Φ1 = 0.05Wb
Current in coil Y, I2 = 5A, Flux produced = Φ2 = 0.075Wb
To find:
Mutual inductance, M
Percentage of flux produced by coil Y and linking with coil X
Formula:
Mutual inductance is given by M = k√(L1L2), where L1 and L2 are the self-inductances of coils X and Y respectively.
The self-inductance of a coil is given by L = (N^2μA)/l, where N is the number of turns, μ is the permeability of the medium, A is the area of the coil, and l is the length of the coil.
Percentage of flux produced by coil Y and linking with coil X is given by (kN2/N1) × 100%.
Calculation:
Self-inductance of coil X, L1 = (N1^2μA)/l
Self-inductance of coil Y, L2 = (N2^2μA)/l
Mutual inductance, M = k√(L1L2)
Substituting the given values, we get:
L1 = (12000^2 × 4π × 10^-7 × A)/l
L2 = (15000^2 × 4π × 10^-7 × A)/l
M = 0.45√(L1L2)
We can calculate the area of the coil using the given data:
Flux produced by coil X, Φ1 = L1I1
0.05 = (12000^2 × 4π × 10^-7 × A)/l × 5
Area of coil X, A = Φ1l/(12000^2 × 4π × 10^-7 × 5)
Similarly, we can calculate the area of coil Y:
Flux produced by coil Y, Φ2 = L2I2
0.075 = (15000^2 × 4π × 10^-7 × A)/l × 5
Area of coil Y, A = Φ2l/(15000^2 × 4π × 10^-7 × 5)
Now we can substitute the values of L1, L2, A, and k in the formula for mutual inductance:
M = 0.45√((12000^2 × 4π × 10^-7 × Φ1l/(12000^2 × 4π × 10^-7 × 5)) × (15000^2 × 4π × 10^-7 × Φ2l/(15000^2 × 4π × 10^-7 × 5)))
M = 0.45√(Φ1Φ2 × l^2/(4π × 10^-7 × 25))
M = 0.45(l/10^3)√(Φ1Φ2)
M
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Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X?
Question Description
Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X?.
Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X?.
Solutions for Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X?, a detailed solution for Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? has been provided alongside types of Two coils, X of 12000 turns and Y of 15000 turns, lie in parallel planes so that 45% of the flux produced by coil X links coil Y. A current of 5A in X produces 0.05Wb while the same current in Y produces 0.075Wb.Calculate mutual inductance and the percentage of flux produced by coil Y and linking with coil X? theory, EduRev gives you an
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