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.
Why fully powering down the device matters hinges on how data is
temporarily stored in it. A typical modem or router has two types of
memory: Non-volatile Memory (NVRAM) and regular old Random Access Memory
(RAM) like the kind in your computer. The router boots off the code
stored in the NVRAM and then uses the RAM just like your computer would
to write temporary variables, execute code, etc. By fully powering down
the device and letting the electrical charges dissipate, the RAM is
wiped and, upon rebooting the device, the micro operating system in the
device has clear RAM to use.
