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Battery Cable size and and speed controller sizes different

Hi, The AWG of the battery is 12 and the speed controller cable looks around 8 AWG. Is it safe for these different size Cables to be connected to power the scooter. The battery has two 10 AWG (Red) cables and two black. So there are 4 cables in total from the battery. There is only one black and one red from the controller though. Is thus a problem? Thanks in advance

As long as there is a fuse or circuit breaker rated at 40 Amps or less installed between the battery pack and controller then 12 AWG wire is a safe size to use. 

If the battery pack has two red and two black wires then two of them could be jumper wires and the other two output wires, or all four wires could be output wires, so that would need to be determined before making the connections. If you could attach a photo of the battery pack then we would be glad to take a look at it and let you know.

Thanks for your reply. Here are the wires on the battery.
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This is at the speed controller end. I'm looking at changing the terminals to XT90s. As you can see the wires of the speed controller are alot thinner than the battery wires.
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The battery pack manufacturer may have run out of thick gauge output wire when they built that battery pack so they used two thinner gauge wires instead. Both of the battery pack's red wires and both of the battery pack's black wires will need to be attached to the new connector.

So is it basically safe if I simply change the connectors to XT90s and solder the 2 red wires together and then attach a 3rd single wire in order to fit it onto the XT90 terminal? (as I don't think the XT90 terminal will fit 2 12gauge wires in). And then do exactly the same with the black? Also when you mentioned about needing a fuse between the battery and speed controller, is that still a must if the scooter already has a fuse installed? If it's still needed then where is best to attach a fuse? I'm not sure as I'm new to this side of things.

I agree that the XT90 terminal is not going to be big enough for the two 12 gauge wires. Only one fuse is needed in the circuit then a second fuse is not necessary. 

Would I be right in thinking this box is where the fuse would be? If so does that mean I won't need one on the battery between the wires?
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The fuse would not be located up near the handlebars like that. It would be in the battery box that is under the footplate. 

I've just seen these under the foot board. I'm not sure if the yellow block is anything to do with a fuse. Or it could be somewhere inside the white plastic trunking in the image?
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The white plastic trunking is too narrow to contain a fuse holder and the yellow junction block only connects the wire terminals together and does not contain a fuse.

This is a 2000w 48v scooter. Do you think it would be unusual not to have a fuse already built in or is that quite common? Do you have any idea where else it could be hidden?

There are no electric scooters which do not have fuses or circuit breakers. On the type of scooter that you have the fuse is usually located on one of the battery pack jumper wires or on the battery pack output wires.

Ok I understand now. I have attached a close up images of the battery connections. Do you know if the fuse is within this section? Or elsewhere. Either way I am cutting that connector off, so will I place the new fuse between one of those wires and the new XT90 connector? Sorry for all the questions but I have to make sure I get this right as it's new to me.
Here is the battery connection
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