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It's my understanding the the purpose of a GFCI circuit is to prevent shock by tripping the circuit if there is an imbalance in current in vs. current out. So my question is, if you have a functioning GFCI circuit, either due to a GFCI outlet or a GFCI breaker in the service panel, is it possible to be electrocuted?

Presuming you had a properly functioning GFCI outlet it would be "safe" to stick, say, a piece of metal into the hot socket while holding the other end? Similarly, if you had a GFCI breaker in the service panel could you "safely" change a light fixture or socket on the circuit without cutting off power to the circuit first.

(I use "safely" in quotes here because I understand you would not want to do this... I'm just curious if this is indeed the case.)

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If you stick a piece of metal in the hot side only, you should not get electrocuted (theoretically). You may, however, get shocked. GFCI's are not instantaneous, and can take up to 25 milliseconds (if I remember correctly) to trip. Also keep in mind "Electrocution" is defined by the stopping of the heart, any electric shock that does not stop the heart is not technically electrocution. –  Tester101 Dec 14 '11 at 20:49
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Yes you can be electrocuted even with an operating GFCI. A GFCI will only trip if current goes from the hot and does not return on the neutral. That means it will trip if you stick a fork into the hot and jump into the bathtub / touch the fridge while holding it (because the current on the hot is NOT seen on the neutral - the power is escaping through the water or fridge chassis to ground).

A GFCI will not trip if you grab one fork in each hand and respectively stick one fork into the hot and another into the neutral (because all the current on the hot is also seen on the neutral). At that point, you're relying on the current operated circuit breaker, which will only trip once the current exceeds its rating (which it may or may not do while going through your relatively high-resistance body).

GFCI's limit shock to a low level, fail often, and are a good supplement (defense in depth). http://www.thecircuitdetective.com/gfis.htm

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So can a person suffer harm from electrocution from a GFCI protected circuit? In the case where the GFCI will not trip, can that hurt a person who is holding the two forks? –  Scott Mitchell Dec 14 '11 at 20:31
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Yes. In the two fork scenario, it will be just like the GFCI isn't there. The circuit will complete across your heart, generate plenty of heat in your hands, and really give you a nasty feeling or cause fibrillation (stopped heart). A circuit breaker only trips after its load has been exceeded. –  Jeff Ferland Dec 14 '11 at 20:33
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@ScottMitchell For the GFCI something/someone has to be electrocuted first. It may not last long, but think of it more as a way to save the second person that comes to your rescue. –  BMitch Dec 14 '11 at 20:40
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+1 on @BMitch's comment -- both a circuit breaker and a GFCI require current to flow before they react. A GFCI reacts faster than a circuit breaker in situations where it will reaction, but they aren't human interfaces to power lines! –  Jeff Ferland Dec 14 '11 at 20:43
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GFCI's also protect against faults in the appliance - think a fridge, or power tool, where the chassis is grounded. If there is a short inside the appliance that connects the hot to the chassis, a GFCI will trip and shut off the power. Without a GFCI, the chassis will still be electrified but at least connected to ground, and likely enough current will flow that the circuit breaker will trip (but as Jeff says, a circuit breaker doesn't act as quickly as a GFCI). If there is no ground, when you touch the chassis YOU will form the path to ground and will be seriously electrocuted. –  gregmac Dec 14 '11 at 21:28
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A GFCI works by making sure that amperage is equal at all times between the hot and neutral sides of the circuit. If this is ever not true, power is "leaking" from the circuit because of a short to ground, either "safely" through an appliance's metal shell to the ground leg of the outlet, or unsafely through you to something else that's earthed like metal plumbing.

A GFCI thus detects MOST situations in which you can be shocked, and will kill the circuit. You will still feel a shock, but it shouldn't be permanently damaging or fatal.

A GFCI will NOT protect you in situations where the current can flow from hot to neutral through you, and so there's no current lost. You can, for instance, get a rough shock by touching a frayed, ungrounded appliance cord (like from a toaster) and contact both sides of the circuit. Unless you're doing this underwater or are also holding your metal sink, there will be little or no "leakage" to earth, and so the GFCI may take longer to register a fault or may not even trip at all.

AFCI breakers (Arc Fault Circuit Interrupters) are one better in certain respects. Instead of simply making sure AHot == ANeutral, they look for patterns of voltage spikes or variance that indicate electrical arcing is occurring. This means that if you were to touch a frayed lamp cord, the high variance in resistance of your skin will cause those patterns and trip the breaker. However, AFCIs are subject to "false positives"; they will trip if you, for instance, plug a vacuum cleaner that is already turned on into an outlet on an AFCI breaker. Other appliances with heavy-duty motors can cause similar false trips. As such they are mainly required only in bedrooms, where electrical arcing can cause a fire right in that room which will be a deadly danger to you long before the smoke alarm in the hall outside goes off.

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The trip setpoints (eg 30mA/20mS) are based on the statistical analysis of electrocutions. (see IEC60479-1) The confidence in this may be >95%. So there is a chance that a person could be electrocuted and the fully functioning GFCI offer no protection whatsoever.

Lesson: To avoid electrocution, don't touch live conductors!

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30mA is ground-fault protection of equipment, ground-fault protection of personnel (commonly found in residential GFCI receptacles) is only 4-6mA. –  Tester101 Jan 8 at 11:09
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