When the number of turns and the length of the solenoid are doubled keeping the area of cross-section same, the inductance

Options

A. half
B. zero
C. two times
D. four times

Answer

C

Explanation

`L=mu_(0)Aln^(2)`
`L=mu_(0)Al((N)/(l))^(2)=(mu_(0)AN^(2))/(l)`
`Lprop(N^(2))/(l)`
`(L_(2))/(L_(1))=((N_(2))/(N_(1)))^(2)xx(l_(1))/(l_(2))`
`(L_(2))/(L_(1))=((2N_(1))/(N_(1)))^(2)xx(l_(1))/(2l_(1))=2`
`therefore L=2L_(1)=`two times.