Given a micro controller with X Volt DC power supply, what is an easy way/rule of thumb to determine how much devices I can connect to the controller (assuming each device requires Y Volt DC)?
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Assuming you mean a microcontroller module, the key circuit is the power supply circuit of the module, not the microcontroller itself.
To be powered directly from the same power supply, the peripherals must all use the same voltage as the supply provides. If it's a 3.3 V supply, the peripherals must all run from 3.3 V.
The number of peripherals that can be powered doesn't depend on the voltage, but on the current drawn by the peripherals. The total of the currents drawn by all the peripherals (in every operating mode or operating condition) must be less than what the power supply is designed to provide.