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I have a whole lot of misconceptions about electricity, and this is one of them. I don't get why the earth wire works; not how, but why. My understanding is that one end of the earth wire is connected to the metal casing of an electrical appliance, so that in case the live wire is in contact with the metal casing and there's current flowing through the metal casing, the earth wire provides a low resistance path to the Earth.

That way, there isn't a danger of getting electrocuted when you touch the metal casing even if the current leaks, because the current is flowing through the earth wire, down to the Earth.

But then I also heard that a circuit needs to be completed in order for an electric current to flow. But in the case of the earth wire, the current is just going into the ground, but it isn't going back to source of the circuit. In that case, why does the current flow through the earth wire in the first place, if it's sort of like a "dead end" and doesn't complete the circuit?

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    $\begingroup$ Possible duplicate: How “earthing” electricity work? $\endgroup$ – lemon Oct 3 '17 at 11:22
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    $\begingroup$ The power grid also is connected to Earth in many places. One of those places quite likely is close to where the wires enter your house. In my home the "neutral" wire is bonded to a long metal stake driven into the ground just below my electricity meter, and it also is bonded to the copper water supply line that enters my house. $\endgroup$ – Solomon Slow Oct 3 '17 at 15:25
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Maybe this link will clear it up for you, an analogy with water circuits.

groundreserv

The reservoir provides a pressure reference, but is not part of the functional circuit. Likewise, the battery can circulate electric current without the ground wire. The ground provides a reference voltage for the circuit, but if it were broken, there would be no obvious change in the functioning of the circuit. The ground wire protects against electric shock and in many cases provides shielding from outside electrical interference.

Also this :

circuit reservoir

It is all a matter of energy carriers in both the water and the electrical circuit. In water it is molecules, once the water circuit has enough water the reservoir is needed only for leaks. It is the pump that supplies the energy to the flow of water. The electric circuit is full of electrons, it is the battery that supplies the energy for the motion of electrons so as to generated a current, which uses the ground as a reference 0 energy difference level (thus no current going through).

but it isn't going back to source of the circuit.But then I also heard that a circuit needs to be completed in order for an electric current to flow. But in the case of the earth wire, the current is just going into the ground

In stable conditions there is no energy going to the ground. Only if by accident instead of 0 volts a voltage appears at the input to the ground wire there will be a current and the circuit will close to the ground by discharging all electrons to the great reservoir of electrons in the ground. There will be a short, and the original circuit no longer works.

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when you touch the metal casing even if the current leaks, because the current is flowing through the earth wire, down to the Earth.

If there is high resistance in the Earth wire then you can have a voltage on case (in the event of a fault). Generally you try and ensure that the resistance throughof the Earth wire is less than the resistance through you - so no current flows through you.

But then I also heard that a circuit needs to be completed in order for an electric current to flow

Not necessarily. If the place the electric current is flowing to is big enough that its voltage doesn't change then it doesn't need to be connected - electricity can just flow into it.

We sometimes use large tanks of salt or large blocks of metal - insulated from the actual ground to act as local Earths in high voltage experiments

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