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The Nintendo Switch uses a USB C charging cable
Yes. The DSi and the 3DS use the same charge cable. As well, the DSi charge cable can be used to power the 3DS' charging cradle too.
cross cable
A USB cable is available for the DS Lite - it connects to the power port on the DS, and allows you to charge up your DS battery from a USB port. You can't use the cable to transfer saves, cheats, or data, however - just charge.
A crossover cable.
If all you want is to play your Nintendo Switch games on your computer’s monitor, you don’t need to connect it to your PC. Most modern monitors have HDMI connectors and are likely to have more than one. So all you need to do is plug your Switch dock into your monitor using an HDMI cable.
The charging cradle is meant to make it simpler to charge your 3DS. Rather than having to grab a charge cable and plug it in, you can just place it in the cradle whenever you're not using it.
cross over cable
It charges the DSi, unless that is a separate cable.
probebly it the same system
Crossover Cable (T568A on one end, T568B on the other)