<p>A generic neural circuit contains capacitor, inductor, resistor and nonlinear resistors, and continuous energy exchange between capacitor and inductor is important for maintaining firing patterns in the electrical activities. When the circuit equations are converted into equivalent dimensionless models as nonlinear oscillators, references for physical time and voltage require the involvement of capacitance. In this paper, two inductors are coupled with a charge-controlled memristor (CCM) for building a reliable neural circuit, noisy disturbance is applied to induce and detect the emergence of stochastic resonance (SR) in the memristive neuron. Because missing of capacitor in the neural circuit, the electric field energy is kept in the inductors and CCM, dimensionless Hamilton energy <i>H</i> is obtained and the curve for its average value &lt; <i>H</i> &gt; vs. noise intensity is effective to predict the SR occurrence under moderate noise intensity, which supports highest mean energy and high regularity in electrical activities. During scale transformation for the physical variables in the circuit equations, reference time is replaced by [L/R], and reference capacitance is replaced by [L/R²], where <i>L</i> and <i>R</i> represent inductance for an inductor and resistance for a resistor. Our results confirmed that effective neural circuits can be built without using a capacitor because of continuous energy exchange among inductors and a memristor. It is much different from the known neural circuits and their derived neuron models with capacitive variables for the membrane potential. It also provides clues to prevent signal termination in neural circuits when the capacitors suffer from breakdown.</p>