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Replacing LEDs...could I damage components?

So I took 2 semesters of physics back in the day, so I THIIIIIINK I know the answer, but given my PC is full of very expensive parts I'd like to just be sure. 

 

I replaced some of the LEDS in a couple case fans in my system (the clear kind which have LEDs built into them). I removed the old LEDs, and soldered new ones in place. It all works fine and I tested it using an old PSU before putting it in my system. 

 

Now. My question is what would happen if my wires touched accidentally. I made sure my solder was fairly clean, and i isolated the exposed cabled with electrical tape so they don't connect, but if they did would the short go back through my 3 pin molex, damage my psu, or even my other components?

 

I dont THINK so for the following reason:

Back in physics I and II I remember that LEDs have very little resistance, and typically you need to put a resistor on the circuit so that the LED doesn't just fry. Because of this, Im imagining that there is some resistance in the circuit already, and even if i did connect the ends, it wouldn't behave any differently than if i had connected the LED. in other words, the difference between connected ends and LED in terms of ohms is super tiny so if short circuiting was an issue it would be an issue with the LED connected normally.

 

Anyway, please let me know if i'm correct. I was very careful to ensure that it doesn't happen just in case, but i'm curious. 

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