  Evolution characteristics of a Kerr black hole (BH) are investigated by
considering coexistence of disc accretion with the Blandford-Znajek process
(the BZ process). (i) The rate of extracting energy from the rotating BH in the
BZ process and that in MC process are expressed by a unified formula, which is
derived by using an improved equivalent cicuit. (ii) The mapping relation
between the angular coordinate on the BH horizon and the radial coordinate on
the disc is given in the context of general relativity and conservation of
magnetic flux. (iii) The power and torque in the BZ process are compared with
those in MC process in detail. (iv)Evolution characteristics of the BH and
energy extracting efficiency are discussed by using the characteristics
functions of BH evolution in the corresponding parameter space. (v) Power
dissipation on the BH horizon and BH entropy increase are discussed by
considering the coexistence of the above energy mechanisms.
