Not quite sure what do you mean by "active charging cable"? Do you have a separate ac wall adapter and usb (full size to micro-usb) cable? Or is it integrated together? Either way it should work perfectly! S4 charger can supply 2A for a full speed charging, while 1st gen N7 charges at 1A and it will *only* sink as much current as it needs. No worries about overheating or anything. I use my 2A Note 2 chargers at home all the time for both of my Nexus 7 tablets.
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