## Introduction

Hello it's a me again Drifter Programming!

Today we continue with **Electromagnetism **to get into **Electric resistance!**

This post might seem similar to the previous post, but it actually isn't exactly the same topic. But you could think about it as some kind of part2 :P

All the mathematical equations will be drawn using quicklatex!

So, without further do, let's get straight into it!

## Resistance definition

Last time we covered that a **conductor that** **obeys Ohm's law** (ohmic conductor) has a special resistance or **electric resistivity ρ** that is given by:

where:

- ρ is the electric resistivity of a conductor
- J the electric current density at some point
- E the electric field that acts inside of the conductor

Of course **ρ is a constant number** (when having an ohmic conductor) and this means that **J is also proportional to E** which can be noted as:

But these equations of course contain only the electric field E and electric current density J and not the electric current I and potential difference V, which we care about much more!

Let's condiser a wire conductor with constant cross-section area A and length L.

The electric current density J and electric field E have the same magnitude for all the points inside of the conductor, which means that the current and potential difference (or voltage) are given by:

You might remember the first one better as:

For the second one think about the equation:

by changing d->L we of course get the equation.

By placing each one in the first equation we get the **voltage**:

An equation that tells us that the **voltage and electric current are proportional to each other** **if ρ is constant **and cause L and A are wire properties.

The ratio V/I for a specific conductor is called **resistance R**:

By replacing the voltage with the previously proven equation we get:

which shows us that **the resistance is constant if ρ is constant** and that the** resistance is proportional to the length L and resistivity ρ, and inverse proportional to the area A**.

Note that the **equation**:

gives us the** resistance for any conductor**, and so even if it doesn't obey Ohm's law, but this formula is called Ohm's law only when talking about an ohmic conductor that has a constant resistance R (which means that ρ is constant).

The **SI unit of resistance is the ohm** (Ω) which is:

(volt/ampere)

but we again will talk about kΩ, MΩ etc. in our examples.

## Resistance and temperature

Because the electric resistivity ρ changes value when the temperature changes, the **resistance R also depends temperature**.

For a small range of temperatures we can **desribe this dependence** using the linear equation (which is the "same" that we had with electric resistivity ρ):

where:

- RT is the resistance at temperature T
- R0 is the resistance for a reference temperature T0
- α is the thermal coefficient of resistance, which has the same value that we had with ρ

The** change of resistance** is given by:

## Resistor in electronic circuits

The electric circuit component with set resistance is called a **Resistor**.

Resistors mostly have:

- a cylinder shape
- diameter of some mm and
- wires (leads) that stick out on every end.

The actual resistance is described by the striped colors that the resistor has:

I actually have played around with resistors and led lights in a course where we covered Arduinos and FPGA's!

Also, note that **resistors have a** **specific endurance/durability**, which is the **maximum voltage that they can consume** without breaking apart.

In electronic circuit diagrams we note them like that:

The **graph of voltage and current** **for ohmic conductors with constant temperature **looks like this:

where the slope of this line is 1/R!

But, for **other conductors** we see more complex shapes which are:

The** relation of current-voltage depends a lot on the temperature**. At smaller temperatures the curve increases mostly faster for positive voltages and the asymmetry of the curve becomes more and more clear.

## Previous posts about Physics

**Intro**

Physics Introduction -> what is physics?, Models, Measuring

Vector Math and Operations -> Vector mathematics and operations (actually mathematical analysis, but I don't got into that before-hand :P)

**Classical Mechanics**

Velocity and acceleration in a rectlinear motion -> velocity, accelaration and averages of those

Rectlinear motion with constant accelaration and free falling -> const accelaration motion and free fall

Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity

Rectlinear motion exercises -> examples and tasks in rectlinear motion

Position, velocity and acceleration vectors in a plane motion -> position, velocity and accelaration in plane motion

Projectile motion as a plane motion -> missile/bullet motion as a plane motion

Smooth Circular motion -> smooth circular motion theory

Plane motion exercises -> examples and tasks in plane motions

Force and Newton's first law -> force, 1st law

Mass and Newton's second law -> mass, 2nd law

Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction

Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications

Contact forces and friction -> contact force, friction

Dynamics of Circular motion -> circular motion dynamics, applications

Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications

Contact force and friction examples -> exercises in force and friction

Circular dynamic and vertical circle motion examples -> exercises in circular dynamics

Advanced Newton law examples -> advanced (more difficult) exercises

**Electromagnetism**

Getting into Electromagnetism -> electromagnetim, electric charge, conductors, insulators, quantization

Coulomb's law with examples -> Coulomb's law, superposition principle, Coulomb constant, how to solve problems, examples

Electric fields and field lines -> Electric fields, Solving problems around Electric fields and field lines

Electric dipoles -> Electric dipole, torque, potential and field

Electric charge and field Exercises -> examples in electric charges and fields

Electric flux and Gauss's law -> Electric flux, Gauss's law

Applications of Gauss's law (part 1) -> applying Gauss's law, Gauss applications

Applications of Gauss's law (part 2) -> more Gauss applications

Electric flux exercises -> examples in electric flux and Gauss's law

Electric potential energy -> explanation of work-energy, electric potential energy

Calculating electric potentials -> more stuff about potential energy, potential, calculating potentials

Equipotential surfaces and potential gradient -> Equipotential surface, potential gradient

Millikan's Oil Drop Experiment -> Millikan's experiment, electronvolt

Cathode ray tubes explained using electric potential -> cathode ray tube explanation

Electric potential exercises (part 1) -> applications of potential

Electric potential exercises (part 2) -> applications of potential gradient, advanced examples

Capacitors (Condensers) and Capacitance -> Capacitors, capacitance, calculating capacitance

How to solve problems around Capacitors -> combination, solving problems, simple example

Electric field energy and density -> Electric field energy, energy density

Dielectric materials -> Dielectrics, dielectric constant, permittivity and strength, how to solve problems

Electric capacitance exercises -> examples in capacitance, energy density and dielectrics

Electric current -> Electric current, current density

Electrical resistivity and conductivity -> Electrical resistivity, conductivity, thermal coefficient of resistivity, hyperconductivity

And this is actually it for today!

Next time I will cover Electromotive Force!

Bye!