It’s just any device where the live circuit has multiple layers of protection to the user.
It does not make grounding not necessary, it just reduces the risk such that no single point of failure will zap you. Regulators have decided that’s “good enough” to reasonably protect you from electrical shock.
Consider a hair dryer. It has an electrical heating circuit where an insulated cable goes into the handle, heats an electrically insulated heater element and gets switched on and off. Now that handle is made of insulating plastic, so let’s just say the wire wears down and touches that plastic, what happens to you? Nothing, because the plastic won’t connect the live wire to your body. It’s double insulated both from the wire touching the handle and the handle “touching” you electrically.
Now what if that handle was made of aluminum instead? Well the live wire wears down and touches the aluminum which touches you which touches the ground and you die. Single insulation.
What if you ground the metal handle then? Well the live wire touches the handle and it has a choice, go through you to ground or go through the metal handle to a ground wire. Well you’re a LOT harder to go through than a copper wire, so most of it goes to ground, and again you’re (probably, don’t try this at home) fine.
Basically, you want several things to have to go wrong for you to die, not just one, and that’s the point of double insulation.
It’s about protection from electric shock to the user of a device. Anything can fail, however the way risk can be reduced doesn’t have to be done one specific way.
Using an earth ground to an appliance or devices metal enclosure is one way. The wires and other parts inside already have basic insulation, sufficient clearances, etc to be generally safe even without an earth ground. However if something does go wrong anyway something inside with the potential to shock someone will contact the grounded chassis which causes a short to ground and a tripped circuit breaker, instead of electrocuting a person touching the device. These are called Class I devices, at least in the US
Double insulation is just that. A second layer of insulation is used to separate a user of a device from the high voltage. It also needs to be a different type, so you can’t just use a thicker layer around wires, which helps prevent both layers failing from the same cause. A plastic case is usually good enough to satisfy the requirement for this. For devices that don’t use too much power this is considered good enough extra protection that it may replace ground from a safety standpoint. This why many smaller power supplies and appliances like cell phone chargers, don’t need an earth ground. These would be a Class II devices. Still, after a certain power level, because of the increased risk you end up needing to use an earth ground anyway.
There’s also class III devices. These are things like laptops which are powered only be a low voltage external supply. Since the device itself doesn’t run on high voltage it doesn’t need either double insulation or earth ground for safety. Instead the responsibility for safety is shifted to the power adapter, does need double insulation.
Cables and circuits inside an appliance is insulated from the rest of the appliance so that the electricity will not flow from a live wire to the chassis or body of the appliance which the user may touch. But if something goes wrong with this insulation you could have a live wire touch the metal that the user is touching which is dangerous. This is why you need to run a ground wire from the parts that the user can touch to the ground to allow any stray current to flow through this wire instead of through the user.
A double insulated appliance however not only insulates the live wires inside it but also the parts that the user might touch. Most commonly today is to make the body of the appliance out of plastic. In this case even if the insulation on the wires and circuit boards may not be working properly the current can not get to the user. So no grounding is necisary.
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