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it will never approach a level of 1. Those coils with low coefficients of
coupling are said to be loosely coupled.
For the secondary, we have
e s � N s
df m
� dt
� N s
and es � kNs � (volts, V) (21.6)
dfp
�
dt
The mutual inductance between the two coils of Fig. 21.1 is determined
by
M � Ns � dfm
�
d
(henries, H) (21.7)
or M � Np � (henries, H) (21.8)
dfp
�
d
Note in the above equations that the symbol for mutual inductance
is the capital letter M and that its unit of measurement, like that of
self-inductance, is the henry. In words, Equations (21.7) and (21.8) state
that the
mutual inductance between two coils is proportional to the
instantaneous change in flux linking one coil due to an
instantaneous change in current through the other coil.
In terms of the inductance of each coil and the coefficient of coupling,
the mutual inductance is determined by
M � k�L� pL� s�
(henries, H) (21.9)
The greater the coefficient of coupling (greater flux linkages), or the
greater the inductance of either coil, the higher the mutual inductance
between the coils. Relate this fact to the configurations of Fig. 21.2.
The secondary voltage e s can also be found in terms of the mutual
inductance if we rewrite Eq. (21.3) as
es � Ns��� dip �� dt �
and, since M � N s(df m/di p), it can also be written
i p
i s
es � M � dip
�
dt
df m
dkf p
� dt
(volts, V) (21.10)
Similarly, ep � M � (volts, V) (21.11)
dis
�
dt
di p
MUTUAL INDUCTANCE ⏐⏐⏐ 937