A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.
RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The four most common RC filters are the high-pass filter, low-pass filter, band-pass filter, and band-stop filter.
Introduction
There are three basic, linear passive lumped analog circuit components: the resistor (R), capacitor (C) and inductor (L). These may be combined in: the RC circuit, the RL circuit, the LC circuit and the RLC circuit with the abbreviations indicating which components are used. These circuits, between them, exhibit a large number of important types of behavior that are fundamental to much of analog electronics. In particular, they are able to act as passive filters. This article considers the RC circuit, in both series and parallel as shown in the diagrams.
Natural response
The simplest RC circuit is a capacitor and a resistor in series. When a circuit consists of only a charged capacitor and a resistor, the capacitor will discharge its stored energy through the resistor. The voltage across the capacitor, which is time dependent, can be found by using Kirchhoff's current law, where the current through the capacitor must equal the current through the resistor. This results in the linear differential equation
Solving this equation for V yields the formula for exponential decay:
Where V0 is the capacitor voltage at time t = 0.
The time required for the voltage to fall to is called the RC time constant and is given by
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