The equivalent inductance of two inductances is `2.4` henry when connected in parallel and `10` henry when connected in series. The difference between the two inductance is

Options

A. 5H
B. 4H
C. 3H
D. 2H

Answer

D

Explanation

Given `L_(P)=2.4 H, L_(S)=10H`
Let `L_(1) and L_(2)` be the two inductance.
We use the laws of series and parallel resistances for `L_(1)` and `L_(2)`.
then `L_(1)+L_(2)=10 and 1/(L_1)+1/(L_2)=1/2.4`
`:. 2.4 = (L_(1)L_(2))/(L_(1)+L_(2)) :. 2.4 = (L_(1)L_(2))/(10)`
`:. L_(1)L_(2)= 24`
But `L_(1)-L_(2) = sqrt((L_(1)+L_(2))^(2)-4L_(1)L_(2))`
`sqrt(100-4 xx 24)`
`sqrt(100-96) = 24`
`L_(1)-L_(2) = 2H`.