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Question
The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as ______.
Options
l and A increase.
l decreases and A increases.
l increases and A decreases.
both l and A decrease.
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Solution
The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as l decreases and A increases.
Explanation:
The self inductance L of a solenoid depends on various factor like geometry and magnetic permeability of the core material.
L = μrμ0 N2 Al
Where n = N/l (no. of turns per unit length)
- No. of turns: Larger the number of turns in solenoid, larger is its self inductance.
- Area of cross-section: Larger the area of cross-section of the solenoid, larger is its self inductance.
- Permeability of the core material. The self inductance of a solenoid increases μr times if it is wound over an iron core of relative permeability μr.
The long solenoid of cross-sectional area A and length l, having A turns, filled inside of the solenoid with a material of relative permeability (e.g., soft iron, which has a high value of relative permeability) then its self inductance is L = μrμ0 N2 A/l
So, the self inductance L of a solenoid increases as l decreases and A increases because L is directly proportional to the area and inversely proportional to length.
Important point: The self and mutual inductance of capacitance and resistance depend on the geometry of the devices as well as permittivity/ permeability of the medium.
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