In this paper it is shown that the recently proposed port-controlled Hamiltonian systems with dissipation precisely dualize the classical Brayton-Moser equations. As a consequence, useful and important properties of the one framework can be translated to the other. For both frameworks a novel method is proposed to deal with networks containing capacitor-only loops or inductor-only cutsets using the Lagrange multiplier. This leads to the notion of implicit Brayton-Moser equations. Furthermore, the form and existence of the mixed-potential function is rederived from an external port point of view.