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A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)
Correct answer is between '175,180'. Can you explain this answer?
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Verified Answer
A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns...
Given that, μr = 60
N1 = 1200
N2 = 1000
d1 = 5 cm ⇒ r1 = 2.5 cm
l = 100 cm
N1 = 1200
N2 = 1000
d1 = 5 cm ⇒ r1 = 2.5 cm
l = 100 cm
Most Upvoted Answer
A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns...
Given data:
- Solenoid 1:
- Length (l1) = 100 cm
- Diameter (d1) = 5 cm
- Number of turns (N1) = 1200
- Relative permeability (μr1) = 60
- Solenoid 2:
- Length (l2) = 120 cm
- Diameter (d2) = 6 cm
- Number of turns (N2) = 1000
Formula:
The mutual inductance (M) between two co-axial solenoids can be calculated using the formula:
M = (μ0 * μr * N1 * N2 * A) / l
Where:
- μ0 is the permeability of free space (4π × 10^-7 H/m)
- μr is the relative permeability
- N1 and N2 are the number of turns of the solenoids
- A is the cross-sectional area of the solenoids
- l is the distance between the centers of the solenoids
Calculating cross-sectional area:
The cross-sectional area of a solenoid can be calculated using the formula:
A = π * (d/2)^2
Where:
- d is the diameter of the solenoid
For Solenoid 1:
A1 = π * (5/2)^2 = 19.63 cm²
For Solenoid 2:
A2 = π * (6/2)^2 = 28.27 cm²
Calculating mutual inductance:
Using the given formula:
M = (μ0 * μr * N1 * N2 * A) / l
For Solenoid 1 and Solenoid 2:
M = (4π × 10^-7 H/m * 60 * 1200 * 1000 * 19.63 cm²) / 120 cm
= 0.000024 * 60 * 1200 * 1000 * 19.63 / 120
= 23.622 H
Converting the result to millihenries:
M = 23.622 * 1000
= 23622 mH
Conclusion:
The mutual inductance between the two co-axial solenoids is 23622 mH, which falls between the given range of 175-180 mH.
- Solenoid 1:
- Length (l1) = 100 cm
- Diameter (d1) = 5 cm
- Number of turns (N1) = 1200
- Relative permeability (μr1) = 60
- Solenoid 2:
- Length (l2) = 120 cm
- Diameter (d2) = 6 cm
- Number of turns (N2) = 1000
Formula:
The mutual inductance (M) between two co-axial solenoids can be calculated using the formula:
M = (μ0 * μr * N1 * N2 * A) / l
Where:
- μ0 is the permeability of free space (4π × 10^-7 H/m)
- μr is the relative permeability
- N1 and N2 are the number of turns of the solenoids
- A is the cross-sectional area of the solenoids
- l is the distance between the centers of the solenoids
Calculating cross-sectional area:
The cross-sectional area of a solenoid can be calculated using the formula:
A = π * (d/2)^2
Where:
- d is the diameter of the solenoid
For Solenoid 1:
A1 = π * (5/2)^2 = 19.63 cm²
For Solenoid 2:
A2 = π * (6/2)^2 = 28.27 cm²
Calculating mutual inductance:
Using the given formula:
M = (μ0 * μr * N1 * N2 * A) / l
For Solenoid 1 and Solenoid 2:
M = (4π × 10^-7 H/m * 60 * 1200 * 1000 * 19.63 cm²) / 120 cm
= 0.000024 * 60 * 1200 * 1000 * 19.63 / 120
= 23.622 H
Converting the result to millihenries:
M = 23.622 * 1000
= 23622 mH
Conclusion:
The mutual inductance between the two co-axial solenoids is 23622 mH, which falls between the given range of 175-180 mH.
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A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. Can you explain this answer?
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A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. 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 solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. 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 solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. Can you explain this answer?.
A solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. 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 solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. 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 solenoid is 100 cm long, 5 cm in diameter and consists of 1200 turns. The cylindrical core has a relative permeability of 60. This coil is co-axial with another solenoid 120 cm long, 6 cm diameter and 1000 turns. The mutual inductance between these two co-axial coils would be ____ (in mH)Correct answer is between '175,180'. Can you explain this answer?.
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