I understand, however, on that line of thinking you can take every component out of ICs. What I'm asking (in a round about fashion) is what applications are there for MOSFETs with anything other than a resistor between gate and source? Also, how does the resistor value alter the MOSFET's behavior? I know that non-logic MOSFETs can use a pot between G and S to alter the resistance of the D-S path, but in a logic FET, how is this useful?
Thanks for your help!
Let's see... You asked a few questions there!
Unlike a BJT which is a current controlled device, MOSFETs are voltage controlled. The gate on a MOSFET behaves like a capacitor in terms of circuit interaction. This means that when you apply a voltage to it, there will be short period of time where the gate is charging and current is actually flowing into it. During this period the circuit is actually consuming power and draining your batteries. Once the gate is fully charged, current stops flowing (except for a very small leakage current) and the MOSFET stops consuming power from the circuit. The ability to remain in an "ON" state while drawing a nearly negligible amount of power is one of the biggest benefits of working with MOSFETS.
You have probably heard people say that when working on high power electronics, you should short or ground all large capacitors because they could contain dangerous voltage levels in them. Since the original circuit did not provide a path to drain the charge out, they can remain energized for a long period of time. Since the gate on a MOSFET is essentially a capacitor, when you remove a voltage source from it and you don't provide a path to ground for it to discharge, enough charge will remain in the gate to leave the MOSFET in an "on" state. The resistor that you add between the Gate and Source provides a path for the charge to flow when you remove your voltage source from the Gate. A resistor in this configuration is called a "pull-down resistor" since it is pulling the gate to a lower voltage level. Once the charge has drained, the voltage of the Gate will equal the voltage of the source and your MOSFET will be in an "off" state.
The reason why resistors are not designed into the MOSFET package is it defeats the low power benefits that it provides. Without a resistor the leakage current of the gate is usually a good deal less than 100nA (.0000001A) but it will vary by device and gate voltage. In a 5V system with a 10K gate to source resistor you will be using 500uA (plus the original leakage) which is 5000 times more current than you were drawing before. While 500uA doesn't sound like a lot, for low power applications it can be huge. If your device has a lot of of MOSFETS, the power consumption can rise rather quickly.
In your application where you do not directly short the gate to ground, the pull-down resistor will change the time it takes for MOSFET to shut off (fall time). The more resistance between your gate and source, the longer it will take for the gate to discharge. Likewise, when you decrease the resistance, it will shut off faster but with the down side of drawing more current when in normal operation. Shut off time is important especially in higher current applications because while the MOSFET is transitioning from "on" to "off" it is operating in its linear zone which can cause it to dissipate a lot of heat from the load you are connected to. I could elaborate on that a lot more but it would be best to save it for the next lesson. More often than not, it is favorable to turn off the MOSFET as quickly as possible.
Lastly you asked about logic vs. non-logic MOSFETS. The only difference between them is logic MOSFETS require a lower gate voltage to reach their full "on" state. When people use a pot between gate and source, they are usually trying to set up a voltage divider for the gate which would force the MOSFET into its linear region. In the linear region the MOSFET behaves like a resistor. The pot allows it to behave like a variable resistor with current handling capabilities much greater than the pot alone.
I hope that helps to answer some of your questions!