A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 , keeping the number of turns

Question

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3 , keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

TestHub · Accepted Answer

As total length L of the wire will remain constant L = ( 3 a ) N ( N = total turns ) and length of winding = ( d ) N (d = diameter of wire) self inductance = μ 0 ​ n 2 A ℓ = μ 0 ​ n 2 ( 4 3 ​ a 2 ​ ) dN ∝ a 2 N ∝ a [ as N = L /3 a ⇒ N ∝ a 1 ​ ] ​ Now 'a' increased to ' 3 a ' So self inductance will become 3 times

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