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how to connect laptop power cable to a PSU?

I have a laptop hp 8440p and it has this cable with 3 wires inside.
I want to make it work with a regular lab PSU, but it has + and. - only, where do I connect the third cable?
 

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Find a ground point on the laptop mainboard to determine which contact in the socket is ground, through resistance measurement with a multimeter. It's probably the outer contact on the plug, then the contact on the inner sleeve is positive, then the pin on the middle is a data line to ID the power supply - without the data line and connection to the PROM that was in the original PSU, the laptop will probably only work at a reduced speed and not charge the battery.

In other words there is nowhere else to put the 3rd wire, unless you have the original PSU and want to power the PROM subcircuit separately then connect to it.
 
As Dave says, that barrel jack has three connections. A plus, a minus and a sense connection.
You can check yourself with a multimeter to find out which is which. But you will have the external barrel, an internal barrel and a pin connection.
Here is an example picture.
upload_2021-4-10_23-24-28.jpeg
Martin
 
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