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On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2?
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On making a coil of copper wire of length l and coil radius r the valu...
The value of self-inductance of a coil is directly proportional to its size and shape. In this case, we are comparing two coils made of the same wire but with different coil radii. Let's analyze the situation step by step:
1. Understanding self-inductance:
Self-inductance is a property of an electrical circuit or coil that opposes the changes in the electric current flowing through it. It is measured in Henries (H) and is denoted by the symbol L.
2. Relationship between self-inductance and coil parameters:
The self-inductance of a coil depends on various factors, including the number of turns, the size of the coil, and the material used. For a solenoid coil, the self-inductance is given by the equation L = μ₀N²A/l, where μ₀ is the permeability of free space, N is the number of turns, A is the cross-sectional area of the coil, and l is the length of the coil.
3. Comparing two coils:
Let's consider two coils made of the same wire, with the first coil having a coil radius of r and the second coil having a coil radius of r/2. The length of both coils is the same, denoted by l.
4. Analyzing the impact of coil radius on self-inductance:
The cross-sectional area of a coil is proportional to the square of its radius. So, if the radius of the coil is halved, the cross-sectional area becomes 1/4th of the original coil.
Using the equation for self-inductance, we can see that the self-inductance is directly proportional to the square of the number of turns and the cross-sectional area, but inversely proportional to the length of the coil.
When the coil radius is halved, the cross-sectional area becomes 1/4th of the original coil. As a result, the self-inductance of the coil with a radius of r/2 will be 1/4th of the self-inductance of the coil with a radius of r.
Therefore, the value of self-inductance for the coil with a radius of r/2 is L/4, not 2L or L/2.
To summarize:
- When the coil radius is halved, the cross-sectional area becomes 1/4th of the original coil.
- Self-inductance is directly proportional to the square of the number of turns and the cross-sectional area, but inversely proportional to the length of the coil.
- Hence, the self-inductance of the coil with a radius of r/2 will be 1/4th of the self-inductance of the coil with a radius of r, i.e., L/4.
1. Understanding self-inductance:
Self-inductance is a property of an electrical circuit or coil that opposes the changes in the electric current flowing through it. It is measured in Henries (H) and is denoted by the symbol L.
2. Relationship between self-inductance and coil parameters:
The self-inductance of a coil depends on various factors, including the number of turns, the size of the coil, and the material used. For a solenoid coil, the self-inductance is given by the equation L = μ₀N²A/l, where μ₀ is the permeability of free space, N is the number of turns, A is the cross-sectional area of the coil, and l is the length of the coil.
3. Comparing two coils:
Let's consider two coils made of the same wire, with the first coil having a coil radius of r and the second coil having a coil radius of r/2. The length of both coils is the same, denoted by l.
4. Analyzing the impact of coil radius on self-inductance:
The cross-sectional area of a coil is proportional to the square of its radius. So, if the radius of the coil is halved, the cross-sectional area becomes 1/4th of the original coil.
Using the equation for self-inductance, we can see that the self-inductance is directly proportional to the square of the number of turns and the cross-sectional area, but inversely proportional to the length of the coil.
When the coil radius is halved, the cross-sectional area becomes 1/4th of the original coil. As a result, the self-inductance of the coil with a radius of r/2 will be 1/4th of the self-inductance of the coil with a radius of r.
Therefore, the value of self-inductance for the coil with a radius of r/2 is L/4, not 2L or L/2.
To summarize:
- When the coil radius is halved, the cross-sectional area becomes 1/4th of the original coil.
- Self-inductance is directly proportional to the square of the number of turns and the cross-sectional area, but inversely proportional to the length of the coil.
- Hence, the self-inductance of the coil with a radius of r/2 will be 1/4th of the self-inductance of the coil with a radius of r, i.e., L/4.
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On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2?
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On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2?.
On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On making a coil of copper wire of length l and coil radius r the value of self inductance is obtained as L . If the coil of same wire but of coil radius r/2 is made the value of self inductance will be? Is it 2L or L/2?.
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