Electricity is constantly a game of electrons (electron-ics)

• electronics is the branch of physics and technology concerned with the design of circuits using transistors and microchips, and with the behavior and movement of electrons in a semiconductor, conductor, vacuum, or gas.

Where we commonly make use of conductive materials (like platinum, gold, copper) connected between an electron-rich source (-) (commonly known as ground), and an electron-deprived one (+)

If there is a path from - to +, then the system will attempt to equalize itself, as a fundamental process. We take advantage of this in strategic ways in electronics.

The rate at which it does so dependent upon things like how strong is the imbalance (the “pressure” or voltage), and how many electrons can flow through the established pathway at a time (the amperage).

Because we are dealing with typically constant voltage source thus far (3.3v coming off the GPIO pins when enabled), our use of resistors tends to be in a “current-limiting” capacity, basically reducing the flow.

Electronic (and especially digital electronic) components can be very sensitive to how they operate- don't give them enough, they won't activate. Give them too much, and they burn out or are otherwise damaged.

Hooking up an LED without a resistor isn't necessarily damaging because of the 3.3v, but instead the unrestricted current:

using Ohm's law: V = I * R, where 'V' is voltage (measured in volts), 'I' is current/amperage (measured in amperes), and 'R' is resistance (measured in Ohms):

I = V / R

I = 3.3 / 1 (there's some inherent resistance on the conductor itself, plus, we cannot divide by 0) = 3.3 so, without a resistor on your LED circuit to limit the current flow, we see upwards of 3.3 amps flowing through

now: flow is one pathway for heat to be generated, and electronics don't like heat

In electronics, we have things like gauges of wire: the thicker the conductive conduit, the more current it can take

Thinner, less.

This is why, if you've ever been running a power-hungry device on an inadequate power cable, the cable warms up (a sign it is approaching full or fuller saturation). Go far enough above it, and it may get so hot as it melts the protective coating (generally considered, especially if running through the walls in your house, NOT A GOOD THING)

The LED components we're using aren't manufactured to withstand that sort of current.

So instead: we limit it, to bring it in spec for normal operation…

I = V / R = 3.3 / 220 (the 220 ohm resistor we've been using) = 0.015 amps (not all that much, but also in this case, we don't need much)

The LED needs a minimal threshold of power to activate… don't give it enough, it won't light up!

Which is why, if you were to accidentally hook up a higher resistance resistor instead, say the 10k ohm:

I = V / R = 3.3 / 10000 = 0.00033 amps (even less) clearly, this makes it fall well below the activation threshold, so we don't see it light up

Whereas, if we wanted to make it dimmer:

I = V / R = 3.3 / 330 = 0.01 amps

or brighter:

I = V / R = 3.3 / 100 = 0.033 amps

Both 0.01 amps and 0.033 amps are much more likely to be within the tolerable operating range of the LED than some value magnitudes higher (risking damage) or magnitudes lower (not enough to activate it).

What components we use and how we use them depend on the constraints of the environment…

If we only had a 5v source, but still wanted similar brightness on the LED as we do in the 3.3v system with 220 ohm resistor (5v should still be a tolerable level):

R = V / I = 5 / 0.015 = 333.33 ohms

So, if we had a 5v source, and desired that some 0.015 amps of current flow, instead of a 220 ohm resistor, we'd want something in the neighborhood of 333 ohms.

If we instead placed a 220 ohm resistor in that 5v circuit, the LED would be marginally brighter, because there's more pressure but no less resistance:

I = V / R = 5 / 220 = 0.022 amps