RC circuit

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A resistor-capacitor circuit (RC circuit), or RC filter or RC network, is one of the simplest analogue electronic filters. It consists of a resistor and a capacitor, either in series or in parallel, driven by a voltage source.

1 Introduction
2 Abbreviations
3 Parallel circuit
4 See also
5 External links

[edit] Introduction

There are three basic, analog circuit components: the resistor (R), capacitor (C) and inductor (L). These may be combined in four important combinations: 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 behaviour 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.

This article relies on knowledge of the complex impedance representation of capacitors and on knowledge of the frequency domain representation of signals.

[edit] Abbreviations

The Following are basic RC time delay equations

Time Constant (T)= Resistance(R)*Capacitance(C)

RC= Ohms x Farads

 = Volts x Coulombs
   -----   --------
   Amperes x volts
  
 = Coulombs x Coulombs
   --------   --------
   amperes  x  coulombs/seconds
   
  = seconds

[edit] Parallel circuit

Image:Parallel-RC.svg

The parallel RC circuit is generally of less interest than the series circuit. This is largely because the output voltage <math>V_{out}</math> is equal to the input voltage <math>V_{in}</math> — as a result, this circuit does not act as a filter on the input signal unless fed by a current source.

With complex impedances:

<math>

I_R = \frac{V_{in}}{R}\, </math> and

<math>

I_C = j\omega C V_{in}\, </math>.

This shows that the capacitor current is 90° out of phase with the resistor (and source) current. Alternatively, the governing differential equations may be used:

<math>

I_R = \frac{V_{in}}{R} </math> and

<math>

I_C = C\frac{dV_{in}}{dt} </math>.

For a step input (which is effectively a 0Hz or DC signal), the derivative of the input is an impulse at <math>t=0</math>. Thus, the capacitor reaches full charge very quickly and becomes an open circuit — the well-known DC behaviour of a capacitor.