In an electric drive system there are three major components.
The Motor draws amps. How many depends on the motor design and the load. It also has a max amp limit. If it draws more than the max it will melt down.
The ESC has a maximum amp rating. This is how many amps it can control. More than that and it will melt down.
The battery has a maximum amp draw limit. This is how many amps you can draw out of it before damage to the battery occurs. Usually rated as the capacity of the battery times a 'C' number.
How many amps are drawn through the system depends on the motor and the load placed on it. Looking at a Trex for example, a Mega 16/15/3 motor would draw up to 30 amps short term during 3d flight. So you need an ESC that can handle those 30 amps plus a little extra for safety. The battery must be able to supply 30 amps for bursts of a few seconds and at least 20 amps continuous.
Then there is the issue of voltage but that's a seperate issue. The battery voltage determines the voltage of the electric system. It can be from 3.5V for a single Lipoly to 75V for a 20 series lipo.
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