Two pure inductor coils of self inductance L each are connected in series, the net inductance is

When two coils are connected in series, the sane current i is induced in both the coils and total magnetic flux linked with them will be equal to the sum of the flux linked with them individually, i.e.,Φ=L1i+L2i  .......(1)If equivalent inductance be L' thenΦ=L′iHence L′i=L1i+L2ior L′=L1+L2Here L1=L2=L∴L′=L+L=2L