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a wire of fixed length is wound on a solenoid of length l and radius r . its self inductance is found to be L . now if same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be
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a wire of fixed length is wound on a solenoid of length l and radius r...
Self Inductance of a Solenoid

The self-inductance of a solenoid is a measure of its ability to produce an induced electromotive force (emf) in response to a changing current flowing through it. It depends on various factors such as the number of turns, the length, and the radius of the solenoid.

Given Information:
- A wire of fixed length is wound on a solenoid of length 'l' and radius 'r'.
- The self-inductance of this solenoid is denoted by 'L'.

Determining the Self-Inductance of the New Solenoid:
To find the self-inductance of the new solenoid, where the wire is wound on a solenoid of half the length and half the radius, we can analyze the relationship between self-inductance and the physical dimensions of the solenoid.

Effect of Length:
The self-inductance of a solenoid is directly proportional to its length. Therefore, if the length of the solenoid is reduced to half (l/2), the self-inductance will also be halved.

Effect of Radius:
The self-inductance of a solenoid is directly proportional to the square of its radius. When the radius is reduced to half (r/2), the self-inductance will decrease to one-fourth (1/2^2) of its original value.

Combining the Effects:
Since the self-inductance of the new solenoid is affected by both the length and radius, we can multiply the effects together to find the overall change in self-inductance.

If the length is halved (l/2) and the radius is halved (r/2), the overall change in self-inductance can be calculated as follows:

Change in self-inductance = (Change in length) * (Change in radius)
= (l/2) * (r/2)^2
= (l/2) * (1/4)
= l/8

Final Result:
Therefore, the self-inductance of the new solenoid, wound with the same wire on a solenoid of length l/2 and radius r/2, will be equal to L/8, where L represents the self-inductance of the initial solenoid.

Conclusion:
The self-inductance of a solenoid is affected by its length and radius. When the length and radius are halved, the self-inductance is reduced to 1/8th of its original value.
Community Answer
a wire of fixed length is wound on a solenoid of length l and radius r...
2L
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Read the following text and answer the following questions on the basis of the same: TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Why inductance of solenoid is more than the inductance of a solenoid having same number of turns, core of same material and similar size?

Read the following text and answer the following questions on the basis of the same:TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Toroid is a

Read the following text and answer the following questions on the basis of the same:TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.A toroid has _____ inductance, for a given number of turns, than a solenoid with a core of the same material and similar size.

Read the following text and answer the following questions on the basis of the same:TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.Why sound system engineers prefer to use toroidal transformer?

a wire of fixed length is wound on a solenoid of length l and radius r . its self inductance is found to be L . now if same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be
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a wire of fixed length is wound on a solenoid of length l and radius r . its self inductance is found to be L . now if same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be 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 a wire of fixed length is wound on a solenoid of length l and radius r . its self inductance is found to be L . now if same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for a wire of fixed length is wound on a solenoid of length l and radius r . its self inductance is found to be L . now if same wire is wound on a solenoid of length l/2 and radius r/2 , then self inductance will be.
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