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Replacing a GPS battery with a power adapter

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joshua17ss2

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I have a GPS system, i want to install in my car, it was thrown out because the main jack for power hookup broke off taking the solder pads with it. what i would like to do is use the old plug that connects to the light dash and outputs 5 volts. i want to remove the old battery (3.7 volts at 1240maH) and replace it with the power from the adapter directly to the battery input, giving it the power it needs to run and bypassing the broken jack.
My concern is that the DC adapter outputs 5 volts, and the battery was marked at 3.7 volts, i was thinking of using a dropping resistor, but since the battery was listed at 1240 maH, i wasnt sure of the resistor, i know the gps probably only uses a fraction of that at a time,
any advice on what i could use to drop that power and keep this working for a long time would be greatly appreciated.
thanks for looking
 
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