Principle of Minimum absorbed Power (PMP) is defined and demonstrated as a fundamental for electrical circuits in stationary and quasi-stationary regime. By imposing the PMP natural conditions result Kirchhoff Current Law (KCL) and Nodal Method (NM). First aim of this paper is to propose a new formulation of basic forms of circuit equations by substituting the KCL or NM equations with PMP equations. Furthermore this paper proves the co-existence of PMP and of Maximum Power Transfer Theorem (MPTT) as one of the basic concepts of electrical circuit theory. All the above considerations can be extrapolated and demonstrated as a natural sequel to linear magnetic circuits in quasi-stationary state by considering their equivalence with electrical circuits. In this case, by imposing the conditions of Principle of Minimum absorbed Energy (PME) one proves that the equations of Kirchhoff's fascicular Fluxes Law (KFL) and Nodal Method for Magnetic circuits (NMM) are achieved. The numerical examples presented hereinafter refer to classical linear electric and magnetic circuits in quasi-stationary state and prove the originality of the theoretical concepts introduced.