Can I use this adapter for my router:
Input: 150-300v - 50hz 500mA Output: 12.0v -- 1.2A
Adapter instead of this broken one:
Input: 100-240v - 50/60Hz 0.3A Output: 9v -- 0.6A
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You cannot use that adapter because it is outputting more voltage than the original (12v vs. 9v). This has a likely chance of burning out one or more of the components within the router. In order to swap out chargers, 3 things must be the same:
There is some wiggle room in the amperage, but the voltage and tip polarity must match. Tip polarity can usually be seen as a symbol like this:
In this picture, it indicates that the tip is negative. Mixing tip polarities is just as likely to fry your router as using too high a voltage.
If replacing the power supply direct from the manufacturer is too expensive, try an electronics shop like RadioShack. They typically sell universal plugs that can be used for any device. Sometimes they even have selectable voltage and tip polarity.
I wouldn't. It might work depending on whether there's sufficient additional voltage regulation inside your router. But the adapter you're considering using puts out a higher voltage than the original, 12v versus 9v, and stands a good chance of burning up your router with higher current than intended.
(Ohm's law says I = E/R. If the load resistance, R, is constant but you increase the voltage, E, you will increase the current, I.)
If you are going to use another adapter use one with the same voltage and at least the same amperage.
Old output: 9v and 0.6A
New output 12v and 1.2A
The third reason is why you do not want to test this.