Two solenoids of equal number of turns have their lengths and the radii in the same ratio `1 : 2`. The ratio of their self-inductances will be

Options

A. `1 : 2`
B. `2 : 1`
C. `1 : 1`
D. `1 : 4`

Answer

A

Explanation

We know, self-inductance of a solenoid,
`L=(mu_(0)N^(2)A)/(l)=(mu_(0)N^(2)(pir^(2)))/(l)`
So, `(L_(1))/(L_(2))=((N_(1))/(N_(2)))^(2)((r_(1))/(r_(2)))^(2)((l_(2))/(l_(1)))=(1)/(4)xx(2)/(1)=(1)/(2)`