Are there any chances it may damage my computer?
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2It's unanswerable - if it needs to be earthed, then it needs to be earthed, if it doesn't, it doesn't. Use whatever came with it. – May 12 '16 at 08:03
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Actually it came with 3 prong power cord but i needed to extend the cable and i had this 2 prong extension cord so i plugged in my 3 prong cable into 2 prong... is that safe? – john jody May 12 '16 at 08:06
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1Safety earthing was [just discussed](http://electronics.stackexchange.com/questions/233501/how-does-grounding-the-circuit-provides-safety) here. – Dmitry Grigoryev May 12 '16 at 08:23
2 Answers
it came with 3 prong power cord but i needed to extend the cable and i had this 2 prong extension cord so i plugged in my 3 prong cable into 2 prong... is that safe?
It is generally unsafe not to earth equipment which was designed to be earthed e.g. a typical mains-powered desktop computer, as in your question.
This is because, in the event of a fault which causes any exposed metal to become "live", the fuse will not blow, since there will be no large current flowing via that (now missing) protective earth wire. :-( Therefore you could be electrocuted by touching the (now "live") metal case and having any other current path (e.g. through your feet, or other hand etc.) to earth.
Based on your description, please do not extend the 3-core mains cable to your desktop computer, with a non-earthed 2-core cable.

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Your chassis will float to half the mains voltage, 115 Vac in 230 Vac countries and 55 Vac in 110 Vac countries, due to the Y-caps between N-GND-L in the power supply of your computer. This may seem harmful but the current though them are limited by goverment standards to 750 uA. This can hurt you, but not enough to kill you. Your EMI will be very compromised too and you may experience excessive 50/60 Hz hum in audio. Whenever I don't have access to earth, I do it like you and run without but please pay attention/measure when you need to connect things like computer -> stereo/TV/antenna, where you may short this 115 V to anouther local or real ground.

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This incorrect and not safe - the 3rd pin is there for a reason - to provide a ground patch for a device that isn't double isolated. A single failure in the device could be deadly without the earth pin connected. – RJR May 12 '16 at 09:55
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I never said it wasn't there for a reason. I explained what will happen if you run it without earth. Your power supply is also double insulated apart from the Y-caps whch are guaranteed not to fail to short, so any single fault will never bridge L-GND or N-GND. – winny May 12 '16 at 10:24
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How do you know the power supply is double insulated (Class II)? Most standard computer power supplies are not. If it were, it would have come with a two-prong cable. – RJR May 12 '16 at 10:32
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The output side is a Class 2 part of an otherwise Class 1 product. You'd be amazed how many are only relying on the ground to meet EMI but all electrical saftey is taken up in the double (required, but tripple inside the transformer) insulation. I've designed and put several into production myself. – winny May 12 '16 at 10:36
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Hmmm, the ATX supplies I've pulled apart (a few) all had the mains connection wires soldered to the PCB without any extra insulation of the through-hole joins. I don't see how that can be class II with the PCB mounted on standoffs in a metal container. In your case, the wires would have to go straight into the (triple insulated) transformer from an insulated connector. example: http://www.xbitlabs.com/misc/picture/?src=/images/other/atx-psu8/3p2.jpg&1=1 – RJR May 12 '16 at 10:47
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sorry, meant 'mains connection wires' - corrected. Not 250kv powerlines :-) – RJR May 12 '16 at 10:51
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No problem. :-) The mains to the chassis needs to be of adequate distance and/or protected by an isoulator like a sheet of plastic. All cables must be tied or glued too since the soldering itself is no guarantee that it will stay there. Doggy manufacturers might obmit this. You need 2 kV(ac) isolation between all primary/L/N-parts and the chassis/secondary. – winny May 12 '16 at 11:01