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perhaps putting a CRC on board would help with this... along with clear instructions on how to "set the resistor" it would allow...
The maximum input voltage is usually 37V for most LM3X7 types, unless you shop around. As you suspected, the issue is not voltage drop, maximum...
It doesn't work that way. If the heatsinks were at half the max junction temperature, the device would be dead. For a TO-220...