the equivalent inductance of two inductors is 2 4 H when connected in parallel and10 H when connected in series - Physics - Electromagnetic Induction

Question

the equivalent inductance of two inductors is 2 4 H when
connected in parallel and10 H when connected in series The
difference between two inductance is(neglecting mutual induction
between coils)

Komal Jain · Accepted Answer

Let the two inductors be L1 and L2
When the inductors are connected in series
Equivalent resistance,
Ls=L1+L2⇒10=L1+L2⇒L1=10-L2When the inductors are
connecetd in parallel1Lp=1L1+1L2⇒Lp=L1L2L1+L2⇒2
4=(10-L2)L210-L2+L2⇒10L2-L22=24⇒L22-10L2+24=0⇒L22-6L2-4L2+24=0⇒L2(L2-6)-4(L2-6)=0⇒(L2-6)(L2-4)=0therefore,
L2=6 or 4
The two inductors are 6 H and 4 H, therefore the difference between
them = 6 - 4 = 2 H

the equivalent inductance of two inductors is 2.4 H when connected in parallel and10 H when connected in series .The difference between two inductance is(neglecting mutual induction between coils)