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Is 00.01ohm's increasing to 9ohm's over 3 seconds considered short-circuit?

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pesh

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3.7V battery connector on a BT speaker PCB. On the Negative side there are two capacitors (connected to the trace with their Negative side) and a grounding plane. On the positive side an on/off switch. While turned off the resistance i get goes above 20M ohms, but when i turn the switch on i get 00.01ohm's gradually raising to 9ohm's. My concern is - would i short the battery (3.7V lipo) when i connect it to the battery connector and turn the switch on? I also added a glass 1.25A fuse on the positive side of the connector, would that protect the battery in case of a short-circuit ?
 

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Does it measure the same when you reverse the meter leads?
 
Does it measure the same when you reverse the meter leads?
Yep the same thing, starts from 000.3ohms and after 3 seconds it reaches 12ohms and settles there. I still havent gathered the courage to plug the 3.7V battery. Thanks to Pommie explanation i'll make an attemp at turning it on (with a bucked of sand near me xD

P.S. It all started with broken usb charging port... i replaced the port and started assembling the speaker, plugged the speakers, the control board and the battery and then i decided to clean the mess flux residue.. "hm get the heating gun and melt that flux, easier to clean then", so i got some aluminium foil to cover the parts that i didn't need to heat (ICs, Caps etc) without realising that the battery is plugged in... *pew* i made a short between some live point and a ground plane and the damn IC blew. From what's left from the IC i was able to read "LTK5***", Took some searching, but i found the company (korean/chinese) and browsed through their LTK5*** ICs and it turns out that they got 3 models and only one with a solder pad below itself and with 10 pins, it had to be the model of the blown chip! So i ordered 3 of them and i replaced it. After that i checked the resistance while on/off and that 000.3ohms -> 12ohms thing happened and now im super confused and kind of scared xD
 

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