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My electrical knowledge is limiting to say the least. I'm trying to build something, DIY style, to teach myself. It's very simple, let's say I have a circuit and an LED. As long as the circuit is complete, the LED should be off. But as soon as the circuit breaks, the LED should flash.

What components am I looking at to get something like this to work?

I was thinking you have a battery powering the circuit. Since power flows through the path with the least resistance, you put the LED in serial over the switch (that will break the circuit), then as soon as the switch is hit, the LED will flash.

I hope I'm making sense.

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You make some sense. Assuming that by 'flash' you mean the LED to be on continuously, your circuit could be

schematic

simulate this circuit – Schematic created using CircuitLab

A disadvantage is that while the switch is closed the full LED current (and even more) is always drawn. To prevent this, you can use a transistor that can be 'enabled' by a current that is a few orders of magnitude lower than the LED current:

schematic

simulate this circuit

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