Resistor-Capacitor (RC) Circuits: Definition & Explanation

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  • 0:01 RC Circuits
  • 0:43 What Is a Capacitor?
  • 1:42 What Is a Resistor?
  • 2:15 Combining Them in a Circuit
  • 2:57 Decay in an RC Circuit
  • 5:02 Lesson Summary
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Lesson Transcript
Instructor: Sarah Friedl

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Resistor-capacitor (RC) circuits are everywhere because they are useful in our everyday lives. The current in these circuits varies with time, making them both practical and common in many types of electronic equipment.

RC Circuits

By now you should be quite familiar with two simple types of circuits called series and parallel circuits. You may remember that a circuit is any path along which electrons can flow. And just like the names imply, a series circuit connects devices in series (like a string of Christmas tree lights), and a parallel circuit connects devices in parallel (like the outlets in your house).

Of course, circuits can be more complicated than these two basic types. One such type of circuit is an RC circuit, which is a circuit that has both a resistor and a capacitor. This is exactly where the 'R' and the 'C' in the name come from.

What is a Capacitor?

In order to better understand RC circuits, we first need to know more about the two components that define it. A capacitor is two parallel plates separated by an insulator. Similar to a battery, a capacitor has two terminals and stores electrical energy.

When a capacitor is connected to a battery in a circuit, the electrons flow from the battery to the capacitor plate that is connected to the battery's negative terminal. The capacitor plate that is connected to the positive battery terminal does the opposite - it sends electrons back to the battery.

Capacitors can come in all different sizes, and some of them can hold a lot of charge! Capacitors are useful because they can get rid of their charge much faster than a battery can. This makes them good for things like a camera flash that needs to use that charge very quickly. Touch screens on modern smartphones and tablets also employ capacitors, making them quite useful!

What is a Resistor?

The other important part of an RC circuit is the 'R' - the resistor. In an electrical circuit, a resistor passively opposes the flow of current. In other words, it 'resists' the electron flow moving through the circuit. Resistors are all sorts of things - light bulbs, toasters, televisions, and more.

While current in a circuit is directly proportional to the amount of voltage, it is inversely proportional to the amount of resistance. This makes sense because voltage produces current, and resistance, well, resists it.

Combining Them in a Circuit

OK, now that you know what an RC circuit is made of, let's get to the good stuff - the circuit itself. RC circuits are really cool because instead of a steady flow of current, an RC circuit is one in which the current varies over time.

If you ride your bike to work or school you know that you'll be safer when you wear a helmet with a flashing light on it. But what you may not know is that the light flashes because of an RC circuit! The duration of the flash is determined by the resistance and the capacitance in that circuit. For example, a small capacitance would produce a quicker flash, whereas a larger capacitance would produce a slower flash.

Decay in an RC Circuit

But we're getting ahead of ourselves, so let's back up for a minute and go over a few more details of the circuit itself. Let's say we have a simple RC circuit like this. The circuit has a battery, a capacitor, a resistor, and a switch that opens and closes the circuit. When the switch is open there is no current flowing through the circuit so the capacitor does not discharge to the resistor.

A basic RC circuit
Basic RC circuit

If we close the switch and complete the circuit, this allows current to flow and the capacitor to discharge through the resistor.

What's key here is that the discharge of the capacitor is not linear, it's exponential. This means that while the rate of decay is constant, the amount of decay is proportional to its current value and changes over time.

We call the rate of decay of current and voltage the time of decay. This value is represented by the constant τ, which is equal to R*C and is measured in seconds.

This time constant tells you a lot about how charging or discharging will occur in an RC circuit. For example, if you have a large capacitor that can hold more charge, it will take a longer time to charge or discharge it so your time constant τ = R*C will be larger. On the other hand, if your time constant τ = R*C is smaller, this means that you have a faster decay.

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