Electric charge and current response of periodic time-varying signals in an RLC circuit

The existence of a non-vanishing resistance in an RLC circuit connected to a DC battery is known to generate an exponentially–decaying behavior in the electrical charge stored in a capacitor and the electric current flowing across the circuit. Nonetheless, a connection to an AC power supply—particularly, a sinusoidal signal—is known to generate oscillatory terms that are not suppressed for large times. A careful analysis of the charge and the current induced by arbitrary time-varying signals in an RLC circuit is performed. It is shown that such exponential suppression disappears for the particular signals that have been analyzed. Moreover, results show that there exists a phenomenon of charge accumulation that takes place in the capacitor and resistance that slightly changes the behavior of the charge an current from one cycle to the next.