Exact calculation of resonant frequency in a real parallel RLC circuit

Abstract

We study a parallel oscillating circuit consisting of an inductance and a capacitance connected in parallel. It is often assumed that such a circuit is ideal, i.e., the inductance has no internal resistance and there is no current leakage through the capacitor. For such an ideal circuit, the phenomenon of current resonance is well studied, and all the quantities arising in this case have been calculated. However, for a real, not ideal circuit, when calculating its frequency characteristics, it is necessary to take into account the presence of internal resistance of the inductor and current leakage through the dielectric of the capacitor. In this paper, such a real circuit is investigated, for which exact, not known so far, formulas for the resonant frequency and the corresponding amplitude are found. This makes it possible to evaluate exactly the errors arising from the use of various approximate formulas widely used in practice.