## Introduction

This is our second article on basic electronics. We recommend reading the first article on the relationship between Voltage and Current If you have not done it yet.

This time we will be talking about the third main element of electric circuits: Resistors.

As we saw on our last article, voltage and current are related via a third factor called electrical resistance; which, as its name hints, represent the resistance of a material to the pass of electrons. In electrical and electronic designs, electrical resistance is achieved by the use of resistors, a passive component that is added to control the amount of current that flows through certain parts of the circuit.

## Ohm Law

We saw that the ohm law defines the current flowing through a conductor as the product of the potential between its extremes and the inverse of the resistance value. i.e.

I = \frac{V}{R}

What this means for us is, we can actually control the pass of current by varying the physical properties of the conductor; or, since we are using a discrete component with the express objective of limiting current, the resistor.

## Resistance and Conductance

The physical characteristics of a resistor depends of three different values:

Transversal Area (A) of the conductor: We saw that current is the manifestation of a flow of electrons; and, as with other types of flow, the bigger the transversal area of the medium of transportation, the easier it is for a big group of elements to move thought it. Imagine a water pipe: would it be more water traveling through a small thin pipe or a bigger thicker one?.

Longitude (L) of the conductor: This one is simple, the longer your conductor is, the more distance electrons need to travel before coming out the other way.

Resistivity (Rho) of the conductor: This one is a constant of the material me choose to use to build our resistor. Some materials are simply more easy for electrons to travel than others. What are you going to do about it?

Knowing all these three factors, we can then define a conductor’s resistance as:

R = \rho \frac{\ell}{A}

On the other side, we can also define conductors by their conductance instead of resistivity; which we define as the inverse of the resistivity:

G = \sigma \frac{A}{\ell}

Where sigma corresponds to the intrinsic conductivity of the material.

Now, let’s see how we can actually use this to build a resistor.

## How we build a Resistor

Let’s define a conductor of 1 m of longitude and 1 m² of transversal area made of copper with resistivity (ρ) 1.68e−8 Ω·m at 20°C.

This will give us a Resistor of 1.68e-8 Ω.

Therefore, by this equation, if we wanted to build a 1 Ω resistor (V = A) we would need to have ~59,523,809 meters of copper cable. Not very convenient, am I right?

This is why we were forced to look for more practical materials with high enough resistivity that would allow us to build smaller resistors.

## Color Codes and Resistor Value

When building electrical circuits, the most commonly used resistors are these

They are color coded so it is easy to identify their value. Here can find a table that will help you read them:

## Other Considerations

Not all materials are made equal. Power dissipation plays an important factor when choosing the kind of resistor you decide to use. High power circuits require more resistant resistor that won’t burn under strong current flows. As a general rule, the bigger the resistor, the bigger the power dissipation it can sustain.

## Conclusion

Resistor are arguably the most important component in electric and electronic circuits. They are very versatile and accomplish a whole set of functions that go from simply limiting current to heat and light generation. And remember, always make sure you are using the right kind of resistor for your application!