If I cut the trace on the motor shield to minimize the power problems on the Mega, where does the Mega get its power?
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Moved your topic to it's current location as it is more suitable.
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It depends on how it is wired, and with out a schematic I can only guess. Why not start by defining the problem with specifications including a flow chart, schematic, power requirements, and EMI requirements if any. Define what the expected outcome needs to be. Purchase the Arduino cookbook and read it, this will give you some basics. also use the online tutorials and videos available, there are many good ones on this web site. At this point you will be able to define the problem and may have already solved it.