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I've got a small 12v 4A water pump that I want to power from a standard 12v car battery. Which calculations do I need to use to figure out the right gauge of wire and fuses?

How would I calculate whether the pump will burn out if I was to connect it directly to the battery? Do I need a transformer or regulator to keep the current and voltage at 12v and 4A?

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The pump will draw just the current it needs. There is no need for other components, except you should fuse the battery since it can deliver very high currents that could heat the wires to dangerous (red-hot) temperatures if a short occurs.

A typical choice for a fuse might be a 5A slow-blo type. Wiring can be AWG 20 or a bit heavier (lower number) gauge to make it sturdier. Fuse it as close as possible to the battery so it can't be shorted without going through the fuse- usually the positive side is the best to fuse.

Ampacity for chassis wiring of AWG 20 is 11A so it should be fine, but it doesn't hurt to have a bit thicker wire to minimize the voltage drop. If the wires to the pump are long you should use thicker wire.

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