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Sorry about the confusion. I went and reread the passage, and I became confused too. My head was turning two ways at once, and the words followed.
Because portable GFCIs are generally used in hazardous situations... most are used by contractors and tradespeople on work sites... they should be used in grounded situations. Since GFCIs can and do fail, using a metal framed portable saw in the grass and compounding the danger by not providing a ground for the tool is dangerous!
However, portable GFCIs do not need a ground to function, since they are designed the same as stationary ones. In fact, one reason for using a GFCI is to protect a person in case the ground is disconnected!
Remember that GFCIs protect from extreme shock, but slight shocks can occur before the GFCI disconnects the power! Therefore people who might be adversely affected by very slight shocks (people with critical livesaving devices such as pacemakers, for example) should be even more cautious!
I am unsure what the humming noise is, but it can only be a malfunction, even if the unit appears to be working OK. Best to err on the side of caution with electricity. Even though the cause of the noise is unknown, I would suggest replacing the GFCI.
Thanks a lot for allowing me to clarify my remarks.
GFCI's (ground fault circuit interrupters) are electrical outlets that have a protective circuit built into them to help prevent life threatening electrical shocks. (Read our full article on GFCI's)
The easiest way to determine the correct amperage is to select a GFCI with the same amperage as the circuit breaker for that outlet.
The other way is to get a wire gauge checker at the hardware store and determine the size of the wires in the circuit. Turn off the power first, of course! Generally, 15 amp circuits use 14 gauge or larger wire and 20 amp circuits use 12 gauge or large wire. The smaller the gauge, the larger the wire.
I have noticed over the years that many hardware stores only stock 15 amp GFCI's, so you may need to go to an electrical supply house or home store to get the proper sizing for 20 amp appliance circuits.
As you describe the problem, I can see three possibilities. The first is that there is a second "fuse" or circuit breaker box in the basement that you are missing which controls the affected rooms. Sometimes when doing renovations, secondary boxes are added to allow for more electrical circuits rather than replacing the main board. Take a good look around if you are unsure!
The second is that a wire has come loose SOMEWHERE. Since this power loss affects so many outlets it would have to be a wire in either the main panel (a.k.a. "fuse" box) or in another electrical box that acts as a feeder for all these outlets. Repair would require you to turn off the power and manually inspect every likely electrical box for a disconnected wire and properly reconnect it. If you don't have any electrical savvy, though, this could be very dangerous and ill advised! Making the wrong connection could be more than just shocking... it could be deadly. Getting an electrician would be a wise idea.
The other possibility is that the circuit is protected by a ground fault circuit interrupter (a.k.a. GFCI). These nifty devices act as a first line of defense against electrical shock and are normally installed to protect outlets and fixtures in damp locations such as outdoors, garages, near kitchen and bathroom sinks, etc. It is not uncommon for them to be installed in basements or in mixed circuits that include bathrooms.
There are two types of GFCI's. One type takes the place of a wall outlet and has "reset" and "test" switches clearly visible on its face. One of these outlet-type GFCI's can protect a number of other outlets if wired correctly. If one is tripped, the power is restored to the circuit by simply pressing on the "reset" switch until it clicks.
The other type of GFCI is a special circuit breaker in your main panel. The face of the circuit breaker would have a white or colored button labeled "test". To reset it, you must flip it completely off and then back on.
I know you said you checked the "fuses", but I remember that my folks always called the circuit breaker box a "fuse box". Old habits die hard, so just in case you really meant circuit breakers I have included this info (and for all our other readers, too!)
It is possible that your boarders used an appliance such as a hair dryer or a vacuum cleaner that caused the GFCI to mistakenly think an electrical short or "ground fault" had occurred, shutting down the circuit. They should be told about the GFCI so that they can reset it themselves if this happens again. A GFCI that begins to trip frequently may need to be replaced.
I have an article at the website on GFCI's at the following URL: https://www.naturalhandyman.com/iip/infelectrical/infgfi.html.
Respectfully, maybe you are misreading what I said. This is a confusing issue and there is quite a bit of "heat" on each side of it.
If you read my article on GFCIs, I make it very clear that a ground is NOT needed for a GFCI to function properly. However, do you disagree that certain tools and appliances have a third grounding plug for a good reason? Are the manufacturer's crazy... or is there a reason, perhaps related to safety?? Of course there is... it is because these appliances do not meet the UL (Underwriters Laboratory) standards of "double insulation", thus posing a potential shock hazard when the appliance is touched under certain conditions.
Grounding is required in all new electrical work... but there is an "exception" for GFCIs used in "old", ungrounded wiring. As you imply, it is better to have a GFCI in a bathroom than NOT have one... I couldn't agree more.
Obviously cognizant of the potential hazard of using three-pronged appliances in ungrounded circuits, though, the NEC (Nation Electrical Code) requires that ungrounded GFCIs must be identified with a label as "ungrounded". In other words, ignore the warning at your peril. Like the labels on cigarette packs, right?
GFCIs are designed to prevent electrocution, NOT electric shock. In my reading on this subject, there seems to be quite a bit of rancor on whether or not the NEC should allow this grounding exception for GFCIs. It has been demonstrated that the amount of shock a person receives before the GFCI activates can be enough to cause injury or death related to the uncontrollable muscular reaction that can occur. OSHA (Occupational Safety and Health Administration) has also issued directives concerning the use of GFCIs in place of proper grounding in a nursing home that did not have proper grounding.
OSHA, in my opinion, has this one right... it only takes a small shock to cause someone to fall from a stool or ladder or roof. Granted that this OSHA directive does not modify the national code (as of this writing), it is a red flag that should be heeded by everyone who does electrical work, professionally or otherwise.
I am a realist and also at times been a risk-taker. I know people will use GFCIs and not ground them! And many people use those little three-prong adapters and don't attach the grounding wire or lug to the outlet cover screw.
So be it... I can't control other people's reckless behavior. Sometimes I can't control my own! Just as long as they realize they risk a shock hazard when using appliances that require a ground. It is their responsibility to live with the consequences. At the least, they should take the NEC's advice and label the outlet as "ungrounded" or (as a personal option and NOT specifically recommended by the NEC) disable the grounding hole with a nonconductive plug of adhesive or epoxy to prevent needless risk.