A coil is wound as a transformer of rectangular cross section. If all the linear dimension of the transformer are increased by a factor `2` and the number of turns per unit length of the coil remain the same, the self-inductance increased by a factor of

Options

A. 16
B. 12
C. 4
D. 8

Answer

D

Explanation

For a solenoid, self inductance,
`L = (mu_(0)N^(2)A)/(l)` but `n = N/l :. N^(2)=n^(2)l^(2)`
`=(mu_(0) cdot n^(2)l^(2)A)/(l) = mu_(0)n^(2)Al`
If all the dimensions of the frame are increased by a factor 2, then the area is increased by a factor 4 and the length is increased by a factor 2.
`:.` The total increase is 8 times.
`:.` self inductance increases by a factor 8.