Pulling the plug out for 10 seconds

A lot of modern technology contains capacitors! These are like energy buckets, little batteries that fill up when you put a current through them, and discharge otherwise. 10 seconds is the time it takes most capacitors to discharge enough for the electronics they're powering to stop working. That's why when you turn your PC off at the wall, things like an LED on your motherboard take a few seconds to disappear. You probably could wait a different time, but 10 seconds is the shortest time you can be sure everything's discharged.

"I think there are 2 topics going on here within this question:

The value of waiting a period of time after removing the power from an electronic device. YES, 30+ seconds is a good ""average"" time to allow Capacitors, hard drives, RAM memory, etc have the time to power down and be ready for the 'power on' reboot sequence.
The proper way to 'power down' an electronic device. Best 'rule of thumb' is if the equipment has an 'on and off' button or switch USE IT. It's there for a reason. As anyone with the knowledge of how a PC operates knows there are important 'startup' and 'shutdown' sequences the equipment goes thru. Allow the equipment time to power down and power up properly. These sequences are necessary for successful operation. Otherwise stress to hardware, stranded files, bloated 'page files', voltage surges, etc... can cause more problems, on top of the one you are trying to fix."