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If I use a P channel MOSFET as a switch for a battery 9v 0.5Ah controlled by an external power source 12 volt will battery last its shelf time if MOSFET is by off?

Update: I dont mind the leakage of the external power supply.

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Look for the off state leakage current spec for the MOSFET you are using. Usually called Idss or zero gate voltage drain current. Typically it's in the range of a few uA, which isn't a lot of current draw but you would have to evaluate the leakage against the battery capacity to see if it will significantly impact the shelf life. The leakage can increase dramatically with temperature, so if high temperature storage is a possibility be sure to take that into account.

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You always get some leakage current. Read the datasheet for that device and look for "\$I_{DSS}\$" which is known, in their datasheet, as the "Zero Gate Voltage Drain Current".

You can see that even when off there is a leakage of 100-500µA (depending on voltage and temperature).

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