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Resonance instabilities in power systems can be assessed with the positive-net-damping stability criterion. This criterion is a review of the complex torque coefficients method, but it does not provide the frequency of the closed-loop oscillatory modes. This paper presents an alternative approach of the positive-net-damping stability criterion to analyze electrical resonance instability. In this approach, resonance instabilities are identified in feedback systems derived from impedance-based equivalent circuits. The proposed approach is used to characterize the frequency of closed-loop oscillatory modes and identify the physical and control parameters of the system that increase or reduce the damping of these modes. The extension of the proposed approach to study the stability of single-input single-output and multiple-input multiple-output feedback systems is analyzed, and the approach is also compared with other stability methods in the literature. An example of an offshore wind power plant illustrates the theoretical study and compares the proposed approach with different methods to evaluate stability. Time-domain simulations in Power System Computer Aided Design/Electro Magnetic Transient Design and Control (PSCAD/EMTDC) are shown to validate the stability study.