How did anyone ever figure anything out about anything?

Simple! Two ways: 1. By thinking real hard about it (Aristotle and co. were all about that), 2. By looking real hard at what it is you’re lookin at (Me at age 5), 3. A combination of both (Science!)

**Einstein** mostly thought a real hard, whereas most of the other chumps – **Ohm** included – had to scrape by on experimental observations and thinking real hard.

Ohm’s Law describes how **Electric Currents** form across **Electric Potential Differences** in **Conductors **(under constraints – the conductors need to be “Ohmic materials” a.k.a. “follow Ohm’s Law“). It relates **Voltage** with the current, and something called **Resistance** – a property of materials to *resist* electric currents flowing.

How’d Ohm figure it all out? Let’s have a think.

It’s been mentioned before, but the **Drift Velocity** of electrons in an **Electric Field** permeating throughout a conductive material is given by: – and **Electric Current**, by definition, is the amount of electrons flowing through a unit cross section of *whatever,* per unit time.

This can be formulated as follows: -> where is the **Current Density** of a material. It depends on the material properties “n” and “τ”, the amount of electrons per volume, and the **Mean Free Time** respectively.

Ohm thought (I think): (*assuming no average velocity*) And so he put making Where that is the **Conductivity** of the conductor (different for different materials).

That’s Ohm’s Law believe it or not! To get the form we all know and love (if you’ve ever done electronics *ever*) we just find that where “V” is the voltage across a distance of length “L” with electric field “E” – and also that from before.

—> where is the **Resistivity** (reciprocal of the conductivity) of the material, and is the **Resistance** across a potential difference of “V” with current “I”.

Don’t forget that “E” is a vector quantity, so that means “J” is too!