Resistivity

Added: 2026-05-21

[00:00:02]we're going to talk about and Define resistivity here is a resistor and we know that a resistor provides a resistance to current flow but what is it about that resistor that determines the size of its resistance well we know that a resistor provides a resistance to current flow by um providing an obstacle to the flow of electrons so if we have a longer resistor we'll also have more obstacles for the electrons to uh bash into during their their journey and so the resistance overall resistance will go up so is the length L of uh the wire that is that makes up the resistor because a resistor is essentially just a a wire um or some other material which impedes the flow uh if the length goes up then the resistance will go up if we have a higher cross-sectional area so just first of all I'll just draw a short resistor versus a long resistor and of course the resistor is actually a a long piece of wire all curled up inside so back to cross-sectional area if we have a wire which has a small cross-sectional area compared to a wire that has a large cross sectional area more electrons per second will be able to flow through the larger cross-sectional area so as the cross-sectional area goes up the resistance will go down because more uh electrons can flow through that resistor and the final thing that the resistance of a material depends on resistance of a resistor depends on is its resistivity and we give that the symbol row and that's a property of the material itself it can also be dependent on temperature now as the resistivity of a material goes up uh it's basically a property of that material there are more obstacles in that material maybe more densely packed or um the lattice of the material is such that the electrons find it difficult to flow through that so for a material with a higher resistivity you will find that the resistance will go up as well also this temperature dependence if the temperature of the material is higher things are jiggling about inside uh and so that will provide even more of an obstacle for electron flow so as temperature goes up the the resistance will also go up just to put these into mathematical terms for the length we can say that the resistance is proportional to the length for the uh cross-sectional area we can say that the resistance is inversely proportional to the cross-sectional area of course these things can be shown a little more thoroughly a little more mathematically um but for now that's enough for us and the resistivity um the resistance is proportional to the resistivity of the material and when we combine those things to those three things together what we get is an equation which says the resistance is uh equals the resistivity times the length divid by the cross-sectional area and if we rearrange that equation we can say just in terms of resistivity is the resistance times the area on the length and we can use that to uh determine what the units of resistivity are it would of course be ohms Time Square M on the top divided by meters on the bottom which gives us ohm M for the units of resistivity