Capacitive micromachined ultrasonic transducers (CMUTs) operating at the series and parallel resonant frequencies, have shown a great potential in ultrasonic application and in biodetection. However, previous equivalent circuits rarely consider the fitting performance and measurement. This study proposes the establishment of the simplified equivalent circuits for the CMUTs-based device to analyze the electrical properties and the measurement sensitivity in liquid environment. We simulate a circular CMUT cell both in air and water through finite element method via COMSOL software, exploiting the multi-domain coupling method. We analyze the impedance behaviors of the CMUTs array with 100 cells under different direct current bias voltages (2 - 10V). Simultaneously, we successfully investigate the damping effects on the electrical characteristics such as impedance, phase, and quality factor. With the 4-element Butterworth-vanDyke model, two simplified equivalent lumped element models (LEMs) are demonstrated to fit the impedance curves of the CMUTs array around the series and parallel frequencies, respectively. Additionally, the sensitivity is evaluated using the simplified equivalent LEMs to explore the CMUTs array has a high normalized measurement sensitivity of 6.024 ppb/Hz at the parallel frequency.