Why can’t electric cars have the equivalent of an alternator to keep the battery charged?

They do. Regenerative braking is when the motors are in reverse. This means that the motors draw power from the battery to speed up. However, this is not braking. It is braking because it violates the laws of physics. A motor that has less power will be harder to turn. If you’re talking about an alternator to make them self-power forever, those pesky laws will again be in play.

Although this is a bit simplified, a generator and motor are basically the same thing.

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