Page 77 - Basic Electrical Engineering

Now let the total equivalent inductance of the single circuit comprising coil 1
and coil 2 as they are connected as in Fig. 1.16 (a) be L e

The EMF induced in the whole circuit will, therefore, be

Thus, equating the expression for e in (iv) with the total EMFs as in (i), (ii),

(iii), and (iv):

Therefore,

L = L + L + 2M (vi)
1
e
2
When the coils are differentially connected as in Fig. 1.16 (b), the EMF

induced in coil 1 due to di in time dt in coil 2, i.e., in opposition to the

EMF induced in coil 1 due to its self-inductance. Similar is the case of the
EMF induced in coil 2 due to mutual inductance. Thus, for the differentially

connected coil

L′ = L + L − 2M (vii)
1
2
e
Thus, the total inductance of an inductively coupled series-connected coil

circuit can be expressed as

L = L + L ± 2M (1.40)
2
T
1