 If we apply variable voltage through an electric device like these three lightbulbs here, we can observe two interesting patterns. First, if I increase the voltage, it looks like the brightness of the lamps is increasing. It turns out that the power output of a light bulb or a resistor will increase with the voltage. We're going to get back to that a bit later. The second thing that we can observe is if we measure the current and the voltage at the same time and then plot the voltage as a function of the current. So I put the current on the x-axis and I put the voltage on the y-axis and what will happen is we will get a graph that looks like this. So it looks like the voltage is proportional to the current. The more voltage I have, the more current I have, the more current I have, the more voltage I have. This relationship can be written down in the form of voltage is equal to current times a proportionality factor R, which we're going to call resistance. Resistance is a property of an electric device and it's usually measured in ohms for which often we use the Greek letter omega. Now what does this relationship tell us? It tells us that as we observe from the graph, the more current we have, the more voltage we have and the proportionality constant is the slope of my graph. So if I calculate the slope, that would be rise voltage over run current and you see I get actually exactly the same law. This law is called ohms law. So the same person, Georg Ohm, after which we labeled the unit of resistance. Now if I had a device that has twice as much resistance, that would mean I have a slope that is much bigger. So this would be a higher resistance and this would be a resistance that is lower. So if I have a higher resistance for the same voltage, it will only let much less current through than the one with the lower resistance. Now what was the thing with the brightness? Well, the brightness in a direct current scenario turns out to be related to the power. Actually it's a bit more complicated because in a light bulb, most of the dissipated power is actually going into heat and not into light. So what we see is not exactly the power output, but some kind of indication of it. The power, we could calculate it as voltage times the current. And now if we build in ohms law, we could say that my power is equal to the resistance times the current times the current squared. Or if I solve this one for I, if I do I, then I get voltage over R. So I could also say we have voltage squared over R. So all three versions of this equation will give us the power output of the device and then we have to see where this power goes.