  The observed eclipsing time variations in post-common-envelope binaries
(PCEBs) can be interpreted as potential evidence for massive Jupiter-like
planets, or as a result of magnetic activity, leading to quasi-periodic changes
in the quadrupole moment of the secondary star. The latter is commonly referred
to as the Applegate mechanism. Following Brinkworth et al. (2006), we employ
here an improved version of Applegate's model including the angular momentum
exchange between a finite shell and the core of the star. The framework is
employed to derive the general conditions under which the Applegate mechanism
can work, and is subsequently applied to a sample of 16 close binary systems
with potential planets, including 11 PCEBs. Further, we present a detailed
derivation and study of analytical models which allow for an straightforward
extension to other systems. Using our full numerical framework, we show that
the Applegate mechanism can clearly explain the observed eclipsing time
variations in 4 of the systems, while the required energy to produce the
quadrupole moment variations is too high in at least 8 systems. In the
remaining 4 systems, the required energy is comparable to the available energy
produced by the star, which we consider as borderline cases. Therefore, the
Applegate mechanism cannot uniquely explain the observed period time variations
for this entire population. Even in systems where the required energy is too
high, the Applegate mechanism may provide an additional scatter, which needs to
be considered in the derivation and analysis of planetary models.
