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 inductated of a sloenoid,
`L=(mu_(0)N^(2)A)/(l)=(mu_(0)N^(2)pir^(2))/(l)`
where l is the length of the solenoid, N is the total nomber of turns of th solenoid and A sis the area f cross- section of the solenoid.
`:.(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)`
`:.(L_(1))/(L_(2))=((1)/(2))^(2)((2)/(1))=(1)/(2)`