# Capacitance: Units & Formula

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• 0:02 What is Capacitance?
• 1:07 Capacitance Equations
• 3:02 Example Calculation
• 4:30 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain what a capacitor is, define capacitance, and solve simple problems using capacitance equations. A short quiz will follow.

## What Is Capacitance?

Capacitors are an electric device relatively few people know about. But that might be considered surprising, particularly when you realize that practically every electronic device will contain capacitors of some kind. A capacitor is a component that stores charge (stores electrical energy) until it gets full and then releases it in a burst.

There are many reasons why you might want to do that. You might store charge in a capacitor in case you lose external power, so that the device doesn't die instantly, allowing recovery processes to complete. You might want a circuit to get a regular 'pulse' of energy every x amount of time. But, whatever the reason, capacitors come in all kinds of sizes, holding anything from tiny amounts of energy to huge amounts.

Capacitors really are used everywhere: from computers to televisions to high-band pass filters to car starters. Almost every electronic device you use contains capacitors. And the title of this lesson: capacitance is a measure of a capacitor's ability to store charge, measured in farads; a capacitor with a larger capacitance will store more charge.

## Capacitance Equations

The definition of capacitance is given by this equation: capacitance C, measured in farads, equals charge Q, measured in coulombs, divided by voltage V, measured in volts. So, for example, if you connect a 12V battery to a capacitor, and that battery charges the capacitor with 4 coulombs of charge, it must have a capacitance of 4/12, which is 0.33 farads.

If the capacitor had a higher capacitance, it would store more charge when connected to the same battery. Because of this equation, we can see that capacitance is, therefore, measured in coulombs per volt. So, it represents how many coulombs of charge will be stored in a capacitor per volt you put across it.

Okay, but what physically makes a particular capacitor actually have a different capacitance? What decides how much charge it stores? Well, that's based on the actual physical characteristics of the capacitor. So, we have another equation for capacitance that looks like this:

The capacitance of a parallel plate capacitor, a simple capacitor that is just two parallel plates separated by a distance, d, is equal to the relative permittivity of the material between the places, K, multiplied by the permittivity of free space, epsilon-zero, which is always equal to 8.854 * 10^-12, multiplied by the area of the plates, A, measured in meters squared, divided by the distance between the places, d, measured in meters.

Most of that is pretty self-explanatory, but K, the relative permittivity of the so-called 'dielectric' material between the plates is generally either equal to 1 or larger. If there's nothing between the plates, K = 1; if it's air between the plates, then K is pretty much still equal to 1; and if it's a different material, it will be a number greater than one, depending on the exact material.

So, those are our two basic equations for capacitance and, as usual, now it's time to have a go at using them in an example problem.

## Example Calculation

Let's say you have a capacitor of area 0.1 meters squared, with plates 0.01 meters apart, and there's air between the plates. If you connect it to a 9V battery, how much charge will become stored on the plates?

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