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When number of turns per unit length of a solenoid is doubled, its self inductance becomes:
- a)4 times
- b)8 times
- c)Same
- d)Doubled
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
When number of turns per unit length of a solenoid is doubled, its sel...
Concept:
- Self-Induction: Whenever the electric current passing through a coil changes, the magnetic flux linked with it will also change.
- As a result of this, in accordance with Faraday’s laws of electromagnetic induction, an emf is induced in the coil which opposes the change that causes it.
- This phenomenon is called ‘self-induction’ and the emf induced is called back emf, current so produced in the coil is called induced current.
Self-inductance of a solenoid is given by:
Where μo = Absolute permeability, N = Number of turns, l = length of the solenoid, and A = Area of the solenoid.
Explanation:
μo ,I, A are constants. So, we can say that
L = k N2 -- (2)
k is constant, N is the number of turns
L is directly proportional to the square of a number of turns.
If number of turns becomes N' = N2, then inductance
L' = k N'2
⇒ L' = k (2N)2 = k 4 N2 = 4 K N2
⇒ L' = 4 L
L = k N2 -- (2)
k is constant, N is the number of turns
L is directly proportional to the square of a number of turns.
If number of turns becomes N' = N2, then inductance
L' = k N'2
⇒ L' = k (2N)2 = k 4 N2 = 4 K N2
⇒ L' = 4 L
So, the inductance is increased by 4 times.
Hence the correct option is 4 times.
Hence the correct option is 4 times.
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Community Answer
When number of turns per unit length of a solenoid is doubled, its sel...
The self-inductance of a solenoid depends on its physical characteristics, such as the number of turns per unit length, the cross-sectional area, and the length of the solenoid. In this case, we are considering only the effect of doubling the number of turns per unit length on the self-inductance.
Self-inductance is a property of a circuit element that resists changes in the current flowing through it. It is typically represented by the symbol L and is measured in henries (H). When the current through a coil changes, an induced electromotive force (emf) is generated that opposes the change in current. This induced emf is directly proportional to the rate of change of current and the self-inductance of the coil.
When the number of turns per unit length of a solenoid is doubled, it means that there are now twice as many turns for the same length of the solenoid. This increase in the number of turns increases the magnetic field produced by the solenoid when a current passes through it.
Here is the explanation of why the self-inductance becomes 4 times:
1. Magnetic field strength:
- The magnetic field strength inside a solenoid is directly proportional to the number of turns per unit length and the current flowing through the solenoid.
- When the number of turns per unit length is doubled, the magnetic field strength is also doubled.
2. Magnetic flux:
- The magnetic flux through a solenoid is directly proportional to the magnetic field strength and the cross-sectional area of the solenoid.
- When the magnetic field strength is doubled, the magnetic flux through the solenoid is also doubled.
3. Self-inductance:
- The self-inductance of a solenoid is directly proportional to the square of the number of turns and the magnetic flux.
- When the number of turns per unit length is doubled, the self-inductance becomes four times (2^2) its original value.
Therefore, when the number of turns per unit length of a solenoid is doubled, its self-inductance becomes four times its original value.
Self-inductance is a property of a circuit element that resists changes in the current flowing through it. It is typically represented by the symbol L and is measured in henries (H). When the current through a coil changes, an induced electromotive force (emf) is generated that opposes the change in current. This induced emf is directly proportional to the rate of change of current and the self-inductance of the coil.
When the number of turns per unit length of a solenoid is doubled, it means that there are now twice as many turns for the same length of the solenoid. This increase in the number of turns increases the magnetic field produced by the solenoid when a current passes through it.
Here is the explanation of why the self-inductance becomes 4 times:
1. Magnetic field strength:
- The magnetic field strength inside a solenoid is directly proportional to the number of turns per unit length and the current flowing through the solenoid.
- When the number of turns per unit length is doubled, the magnetic field strength is also doubled.
2. Magnetic flux:
- The magnetic flux through a solenoid is directly proportional to the magnetic field strength and the cross-sectional area of the solenoid.
- When the magnetic field strength is doubled, the magnetic flux through the solenoid is also doubled.
3. Self-inductance:
- The self-inductance of a solenoid is directly proportional to the square of the number of turns and the magnetic flux.
- When the number of turns per unit length is doubled, the self-inductance becomes four times (2^2) its original value.
Therefore, when the number of turns per unit length of a solenoid is doubled, its self-inductance becomes four times its original value.
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