I Accidentally Apply A 12V AC To A 9V DC Modem And The Adapter Got OverHeated And Dead...But Why? Then I Use A 9V DC To A 12V AC Modem..Its Working Fine..I Just Wish To Know Why A 12V AC Adapter Got Killed? Anyone Know?

 

If the device is built to operate on DC, then the diodes and other polarized components are built to operate in one direction.

AC runs in 2 directions so you could have been running devices near their breakdown point for reverse voltages. That is what probably killed it.

 

The 9V DC modem is expecting its power to be properly prepared and delivered as DC. It is built inside to only be safe with one polarity of voltage. This means that large filter capacitors are ready to receive only one polarity, and they short circuit if fed the wrong polarity.

The AC modem is prepared to correct AC into DC, no matter which polarity arrives. Each polarity is sent through diodes to the correct side of each capacitor. When you deliver DC to an AC modem, it simply routes the DC to the correct capacitor.

But when you feed AC to a DC modem, the wrong polarity is not routed through diodes to the correct side of the capacitors. Then the capacitors short circuit and kill the Adapter.

 

Modems aren't the sexy devices they used to be, but a large percentage back in the day used simple AC adapters, they were designed for it. You need to look as the specs of the modem in question. What is the make and model?