Electronics/RC

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Introduction

An RC circuit is short for 'Resistor-Capacitor' circuit. A capacitor takes an infinite amount of time to discharge through a resistor, which varies with the values of the resistor and capacitor. A capacitor acts interestingly in an electronic circuit, practically speaking as a combination of a voltage source and a variable resistor.

Basics

Below is a simple RC circuit:

There is a capacitor in parallel with the resistor and current probe. The way the capacitor functions is by acting as a very low resistance load when the circuit is initially turned on. This is illustrated below:

Initially, the capacitor has a very low resistance, almost 0. Since electricity takes the path of least resistance, almost all the electricity flows through the capacitor, not the resistor, as it has considerably higher resistance. As a capacitor charges, its resistance increases as it gains more and more charge. As the resistance of the capacitor climbs, electricity begins to flow not only to the capacitor, but through the resistor as well:

Once the capacitor's voltage equals that of the battery, meaning it is fully charged, it will not allow any current to pass through it. All the electricity eventually flows through the resistor.

A capacitor's resistance becomes higher and higher as it becomes more charged. Once it is fully charged, for all practical reasons, it has infinite resistance (an open connection). Once the voltage source is disconnected, however, the capacitor acts as a voltage source itself:

As time goes on, the capacitor's charge begins to drop, and so does its voltage. This means less current through the resistor:

Once the capacitor is fully discharged, you are back to square one:

If one were to do this with a light and a capacitor connected to a battery, what you would see is the following:

1. Switch is hit. Light does not light up.
2. Light gradually becomes brighter and brighter...
3. Light is at full luminosity.
4. Switch is released. Light continues to shine.
5. Light begins to fade...
6. Light is off.

This is how a capacitor acts. However, what if you changed the values of R1? C1? The voltage of the battery? We will examine the mathematical relationship between the resistor, capacitor, and charging rate below.

The Time Constant

In order to find out how long it takes for a capacitor to fully charge or discharge, or how long it takes for the capacitor to reach a certain voltage, you must know a few things. First, you must know the starting and finishing voltages. Secondly, you must know the time constant of the circuit you have. Time constant is denoted by the Greek letter 'tau' or τ. The general formula for percentage change is: