That's normal. It's the A/C compressor clutch cycling.
I don't see why your voltage issue would have anything to do with your A/C compressor cycle time. It cycles based on system pressure and is controlled by pressure switches. 10 seconds seems a little long for it to cycle, but if the A/C is cold I wouldn't be concerned. Mine cycles maybe every 8 seconds, but it will vary depending on outside temperature. If you A/C is slightly low on refrigerant it could be increasing the cycle time, but you'd need a set of A/C gauges and a temp/pressure table to determine that. Like I said, if it's cold I wouldn't worry about it.