Sheet resistance seems to me rather counter-intuitive, but I suppose it's analogous to the way that the pressure of a fluid is only dependent on depth? Grid resistance...looks pretty complicated. Found some material such as
this and
this, but that's all just way over my head at this point. But thanks for the thoughts, anyway, very interesting stuff.
Hi,
Well it's interesting that when we connect four resistors in a certain way we get the same resistance as one resistor.
However, it does not stop there. If we call that new resistor (made from the 4 resistors) Rn1, then when we connect four of THEM in the same manner, we again get the same resistance which was the original resistance for one resistor.
Now continuing in this manner, we can build a network of many resistors that still end up being the same value as just one but the construction gets bigger and bigger.
Yes the sheet resistance is two dimensional so it's a little different. What might be interesting is to build a grid using the above method and then start to measure resistances inside the construction not just at the two ends that form that one big resistor.
We can look at the heat dissipation vs surface area too which forms a simple relationship.
When we have a resistor R1 with surface area S1 and power dissipation P1 that results in a temperature T1 in an environment at ambient temperature, when we increase the network to four resistors all the same value as before, the surface area goes up to 4*S1 and in this case the surface area went up in a linear fashion so the heat distribution is linear so we get power dissipation P1/4, or stated another way we can get power dissipation 4*P1 now.
That's not how things usually work though, because the volume vs surface area vs power comes into play where when we increase the volume we dont increase the surface area enough, when it is all in the same package. So the individual packages allow a more even spread of the heat which is nice.
I find that in real life applications i dont like to run the resistors at too high a temperature because they might melt the plastic case usually used with todays' stuff. I did a battery charger one time that had to charge twice a day automatically and used a 10 ohm single power resistor. I placed the resistor outside the case so that it could get free air flow and kept the dissipation down low for the size. I cant remember the numbers now but it was something like a 10 watt resistor dissipating just 1 watt.
Also you may find interesting is there are more strict limits when we confine the resistor where it can not get free air flow.
In theory, if we place a resistor in a confined perfectly sealed container where no heat can get out and fun that resistor at 1 microwatt, the temperature will eventually reach an infinite value which would melt any substance we know of. This basically says that all resistors must have some means of cooling from the outside world. This usually means a vent in the case if there is significant power dissipation.