Well in my experience, the LEDs have very minimal resistance compared to an actual resistor. I forget what I measured, but it was a small percentage. The batteries don't have a huge internal resistance either.
LED's don't have a fixed resistance, they are nonlinear devices. Current through them increases exponentially with the voltage applied to them. This means that their resistance changes dramatically depending on the circumstances. If you apply a low- or reverse- voltage to them, their resistance will be effectively infinite (zero current). If you apply a high voltage, their resistance will be effectively zero (extremely large current).
Don't think of LEDs as resistors at all. A more useful model is to assume that the LED will drop a certain fixed voltage, usually referred to as the Vf in your LED data sheet.
Let's say the Vf of your LED is 3.5V (a fairly typical value). Let's say battery internal resistance is 0.5V Expected current would then be:
I = V / R
V = Vbatt - Vdiode = 4.5 - 3.5 = 1
R = R + Rbatt = 0.3 + 0.5 = 0.7
I = 1/0.5 = 1.4A
This may sound high, but in all likelyhood, your alkalines voltage will drop and internal resistnace will rise as they drain, so this could easily settle to around ~0.7A for most of the runtime. It is also possible that the LEDs being used in this case are ones with higher Vf (say 3.8V), and that there is even more resistance elsewhere in the system (such as in the LED leads, wire traces etc), such that the total system resistance is more like 1 ohm:
I = (4.5-3.8) / (1) = 0.7 amp peak
To find out what the Vf of your LED is, simply measure the voltage drop across it while the LED is on sometime When I build direct-drive flaslhights, what I will actually do is hook up my LEDs to my bench power supply, then use the current limiter to set the current to my goal current for the project -- that way i can instantly see what the Vf of my LED is. Then I will know whether my choice of battery and resistor (or regulator) is suitable before installing anything.
If the resistors were just plain wires, too much current would flow and likely burn up the LEDs right? Once they burn out idk if they short circuit or open... am I missing something?
If running on Alkaline batteries, you might be able to still survive even with no extra resistance. Those have very high internal resistance. However, If you were to throw something like NiMH cells in your light (which have almost no internal resistance) you might cook the LEDs. Or you might be fine. Depends on the Vf of the LEDs:
Let's say your LED Vf is 3.8, and you drop in a few fresh NiMH Cells (1.4V hot off the charger):
I = (4.2 - 3.8) / 0.3 Ohms = 1.33 Amps. Not great for longevity, but the LEDs may live.
Now let's assume your LED Vf is actually 3.3:
I = ( 4.2 - 3.3 ) / 0.3 Ohms = 3 Amps. Cooked.
