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. `2` henry
B. `3` henry
C. `4` henry
D. `5` henry

Answer

A

Explanation

`L_(s)=L_(1)+L_(2)=10H` …..(i)
`L_(p)=(L_(1)L_(2))/(L_(1)+L_(2))=2.4H` ……(ii)
On solving (i) and(ii)`L_(1)L_(2)=24`
Also `(L_(1)-L_(2))^(2)=(L_(1)+L_(2))^(2)-4L_(1)L_(2)`
`implies(L_(1)-L_(2))^(2)=(10)^(2)-4xx24=4impliesL_(1)-L_(2)=2H`