The self inductance of a coil is L . Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be

Options

A. `(1)/(4)L`
B. L
C. 4 L
D. 16 L

Answer

D

Explanation

Self-inductance of coil is directly proportional to squre of number of turns in the coil, i.e.,
`L propN^(2)`
`therefore" "(L_(1))/(L_(2))=(N_(1)^(2))/(N_(2)^(2))`
`therefore" "(L)/(L_(2))=(N^(2))/((4N)^(2))`
`therefore" "L_(2)=16L`