What is the aim of 100ohm resistor between the micro-controller pin and the gate of the N-channel MOSFET?
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The 100 Ohm resistor on the gate of the N-Channel MOSFET is there to stop any potential ringing. Ringing is caused by gate capacitance in series with the inductance of the track/wire.
The 10k resistor is just a pull-up resistor to keep the gate of the P-Channel MOSFET high. Or so I assume as you haven't actually labelled the nodes of the P-Channel. Once the MCU pin goes high, the N-Channel MOSFET turns on, which pulls the gate of the P-Channel MOSFET low, turning it on and allowing current to flow through it.

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Is it worth explaining the finite turn-off time as a function of the pull-up value? – AaronD Dec 30 '20 at 20:40
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@AaronD I'd say not. Looking at the nature of the question, it's clearly a beginner level question. So they deserve answers that don't overcomplicate things in my opinion. It's likely not going to be of much use at this level – MCG Jan 01 '21 at 22:20