Trying to better understand voltage and current sources
I understand that these &quot;ideal&quot; sources are ideal and don't exist in practice.

They do to a point. Voltage regulators maintain constant output voltage up to some maximum current.

In reality there is always some resistance.

No. The voltage regulator will maintain the voltage across a range of current draw. Since \$ \frac {dV}{dI} = 0 \$ over that range of current then its output impedance is zero.

What I don't understand is why then are are able to switch between them, ...

Switch between what?

... or how we can talk about insensitivity to load changes when Ohm's Law says V = IR, if I have a voltage source, is that not fixed?

Yes. So if I connect a 1k load across a 5 V supply I draw 5 mA. If I connect a 100 Ω load across the same supply I draw 50 mA. The voltage remains at 5 V. It is ideal up to the designed current limit of the PSU.

And then if I add a bigger resistor, doesn't that mean less current must flow in turn?

For a constant voltage supply, yes.

Or for a current source, if I change the resistor, am I not then changing the voltage?

Yes, of course.

Figure 1. A random bench PSU image.

I have a bench power supply with an adjustable current limit on it. If I set the current limit to 20 mA and the voltage limit to 30 V and switch it on, the voltage will rise to 30 V in an attempt to push 20 mA between the terminals. It can't. The air's resistance is too high.
If I now connect a red LED between the terminals the current will rise to 20 mA and the voltage will fall to about 2 V.
If I now connect 12 red LEDs in series to the terminals the current will still be 20 mA and the voltage will rise to about 24 V.

The power supply is operating as an ideal current source for loads between 0 Ω and 30 V / 20 mA = 1.5 kΩ. Since the current remains constant over that voltage range we get \$ R = \frac {dV}{dI} = \frac {dV} 0 = \infty \$.

And since I am able to change the other variable, why are we then able to swap between them?

Again, it's not clear what you are asking here.

Can anyone please give a few examples showing these &quot;ideal&quot; forms, why they are unrealistic, why we are somehow able to switch between them, and what a &quot;real&quot; example might look like?

They're not unrealistic over a certain range of operating conditions. I'm still not clear what you're switching between. I've given an example.


By &quot;switching&quot; I refer to when people say you can transform a voltage source into some equivalent current source and vice versa.

For a fixed resistance you can supply a load with constant voltage or constant current. If the resistance can change then you need to choose one or the other depending on what you want to happen.
In most applications you can't switch a CV supply for a CC one or vice versa. Most circuitry is designed to work on a constant voltage. The national grid (even though it's AC) is designed on this basis. Cars, buses, airplanes, phones, computers and most &quot;electronics&quot; are designed to work on a particular voltage. The most common exception is LED lighting where constant current supplies are used due to the shape of the LED's IV curve.