Let us take a look at why electric cars don't have multiple gear transmissions.
Why don't electric cars have multiple gear transmissions like you would find in more traditional internal combustion engines? Well, there are numerous reasons as to why this is, but the main reasons are because electric cars are much higher revving engines. They also remain highly efficient across a wide RPM range, as well as they are able to produce sufficient amounts of torque at lower RPM's.
Whereas internal combustion engines need a transmission gear ratio of around 4:1 to provide sufficient torque at lower RPMs and speeds, the higher revving electric motors don't suffer from the same characteristics and, therefore, are able to provide sufficient power and torque throughout their different driving speeds.
However, this doesn't mean that there is no room for gears in electric cars at all, it all depends on the use of the car. For normal road-going cars, one gear is more than sufficient, but having one gear limits the top speed, in Formula E there are electric race cars that make use of a few gears in order to reach higher driving speeds.
Take a look at the video below by YouTube channel, Engineering Explained, on Why Electric Cars Don't Have Multiple Gear Transmissions.
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