Upgrading Electical Grounding

I have an older house in which the electric cables to all the switches and receptacles have only 2 wires: one black (hot) and one white (neutral). I would like to upgrade the receptacles to the newer type that have a third opening in them for a ground. I would like to avoid running new cable with three wires (black, white, ground) as this would be a fairly tough job to fish new cable through the walls. The new cable is also pretty expensive.
Is it acceptable to just run a ground wire (either bare or green) from the ground bar in by service panel to the receptacles. In many locations this would be easier than fishing a whole new cable as well as less expensive.
Thanks in advance for any guidance.
Herb
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Are the existing cables non metallic?

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Yes, they are non-metallic.

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Yes, they are non-metallic.

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Herb S wrote:

Then, IIRC, you can do as you propose since the cable is nonmetallic. Use Tyraps to secure the equipment grounding wire to the existing cables as much as possible. It's a lot of work. Using GFCI receptacles at the first outlet in each circuit would be a lot easier. All downstream receptacle outlets could then be 3 prong.
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"install a GFCI receptacle. The ground lug      should not be connected to anything, but the GFCI      protection itself will serve instead. The GFCI      will also protect downstream (possibly also two prong      outlets). If you do this to protect downstream outlets,      the grounds must not be connected together. Since it      wouldn't be connected to a real ground, a wiring fault      could energize the cases of 3 prong devices connected      to other outlets. Be sure, though, that there aren't      indirect ground plug connections, such as via the sheath      on BX cable.
    The CEC permits you to replace a two prong receptacle with a three     prong if you fill the U ground with a non-conducting goop.     Like caulking compound. This is not permitted in the NEC.
    The NEC requires that three prong receptacles without ground     that are protected by GFCI must be labelled as such." this and more at: http://www.faqs.org/faqs/electrical-wiring/part1 /
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: "install a GFCI receptacle. The ground lug : should not be connected to anything, but the GFCI : protection itself will serve instead. The GFCI : will also protect downstream (possibly also two prong : outlets). If you do this to protect downstream outlets, : the grounds must not be connected together. Since it : wouldn't be connected to a real ground, a wiring fault : could energize the cases of 3 prong devices connected : to other outlets. Be sure, though, that there aren't : indirect ground plug connections, such as via the sheath : on BX cable. : : The CEC permits you to replace a two prong receptacle with a three : prong if you fill the U ground with a non-conducting goop. : Like caulking compound. This is not permitted in the NEC. : : The NEC requires that three prong receptacles without ground : that are protected by GFCI must be labelled as such." : this and more at: : http://www.faqs.org/faqs/electrical-wiring/part1 / :
But, that won't do anything for providing an earth connection for computers, surge protectors, etc. although it certainly DOES add in the safety factor for the GFCI lines.
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I haven't got a current code book handy, but unless something has changed. 250-130 (C) (5) says you can

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wrote:

You can probably be selective about which ones really need a ground. If you don't use 3 prong plugs there, don't bother. Computers, fridges, washing machines, disposals and microwaves should get the ground.
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