The equivalent inductance of two inductors is 2.4 H when connected in parallel and 10 H when connected in series. What is the value of inductances of the individual inductors?

Explanation

As inductances obey laws similar to the ''grouping of resistances''
`L_(1) + L_(2) = 10 H` and `(L_(1) L_(2))/(L_(1) + L_(2)) = 2.4 H`
Subsitituting the value of `(L_(1) + L_(2))` from first expression into the
Second, `L_(1)L_(2) = (2.4)(L_(1) + L_(2)) = 2.4 xx 10 = 24`
so that `(L_(1) -L_(2))^(2) = (L_(1) + L_(2))^(2) - 4L_(1)L_(2)`, i.e., `L_(1) - L_(2) = 2 H`
and as `L_(1) + L_(2) = 10 H`, so `L_(1) = 6 H` and `L_(2) = 4H`