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

Self inductance of a solenoid,
`L = (mu_0 N^2 A)/(l) = (mu_0 N^2 pi r^2)/(l)`
where l is the length of the solenoid, N is the total number of turns of the solenoid and A is the area of cross-section of the solenoid.
`therefore L_1/L_2 = (N_1/N_2)^2 (r_1/r_2)^2 (l_2/l_1)`
Here `N_1 = N_2, l_1/l_2 = 1/2 , r_1/r_2 = 1/2 therefoe L_1/L_2 = (1/2)^2 (2/1) = 1/2`