Microstrip ring resonators with quality factor (Q) over 104 at temperature 5 K, were fabricated using the double-side YBa2Cu3O7-δ (YBCO) epitaxial films deposited on LaAlO3 (LAO) substrates. By placing a narrow gap in the ring resonator, we observed that the original fundamental resonating mode (resonance frequency f = 3.61 GHz) splits into a dual-mode with different resonating frequencies (f = 1.80 GHz and f = 5.33 GHz). These two kinds of the resonator allow us to determine the temperature and frequency dependences of the magnetic penetration depth λ(T, f) and the surface loss. Several salient features of the above findings related to the nature of low-lying excitations for high-Tc superconductivity as a function of oxygen content will be elucidated. In particular, the current models, suggested by Wen and Lee, will be examined in a quantitative manner. It allows us to give a justification of quasiparticle as Fermi-liquid in the superconducting state. In addition, an equivalent inductance circuit model is suggested to account for the occurrence of the dual-mode resonance.