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:

Step-by-step solution

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) array l self inductance = ₀ n ² ~A = ₀ n ² ( 3 a ² 4 ) d N a ² ~N a [ as N = L / 3 a N 1 a ] array Now 'a' increased to ' 3 a ' So self inductance will become 3 times