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This paper introduces a new equivalent circuit for linear direct current networks consisting of independent voltage and current sources, and resistors, which represents all the power dissipated internally in the resistors. It is demonstrated that the internal losses of any network have two components. One is variable and dependent on the internal resistances of the actual circuit and the power transferred to the pair of accessible terminals. The other is constant and dependent only on the internal voltage and current sources and the resistances of the actual network. It is also demonstrated theoretically and validated by numerical simulation that the traditional Thevenin and Norton equivalent circuits are particular cases of the proposed equivalent circuit in this paper. The proposed equivalent circuit can be used to analyze power and efficiencies of the actual network.