Polarity(?) and common house-current

I live in a little house built in 1954. It has a certain number of ungrounded receptacles.
In the context of DC power, I have some notion of the importance of polarity.
For years, all small electrical devices/accessories (i.e. extension cords) with 2-prong male plugs that I've seen have 1 wide and 1 thinner blade. To facilitate connections and minimize hassle, I've been grinding the wider to the width of the thinner blade.
This'll likely qualify as a "naive question". In the context of single-phase power and small ~120v 60 hz AC ("Alternating Current") household devices, what purpose does having 1 blade wider than the other serve?
Thanks, AQ
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The wider prong is the neutral side of the circuit

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Aloysius Q Roger-YoMama wrote:

The wider slot in those recepticals is (per code)connected to the neutral feed conductor. That conductor is nominally at ground potential, though it is not permitted to use it as a ground. Thus, touching that conductor while also touching a grounded pipe will not electrocute you.
As one example, table lamps are (or should be) constructed so that the conductor from the wide blade of the cord plug connects to the "shell" of the bulb socket(s). That way, if you're changing a lightbulb in the lamp, while standing on a wet concrete floor with bare feet, and your fingers happen to touch the screw base of the bulb before it's fully out of the socket, you won't get shocked.
There are numerous other examples of tools and appliances which take advantage of the wide slot being at or extremely close to ground potential, but the light bulb one is easiest to understand.
See:
http://home.comcast.net/~jwisnia18/jeff/screwing.gif
Jeff
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The narrow blade goes into the "hot" slot. The wide one goes into the neutral.
with a polarized plug, you turn the switch off at the appliance, and there is "hot" power up the cord, and to the switch. The rest of the appliance is safe to touch.
With a same size plug, the switch might turn off the power in the appliance, or it might turn off the neutral, leaving the appliance energized all the time. Energized, as "can shock you". Not energized as in "costing your electricity".
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