Electronic – Live wire and ground question

It boils down to current distribution, but let's start from the beginning.

In both cases you form a circuit with several elements in series. Some of them have excellent conductivity, like copper wires. You are of meager conductivity, but your shoes and ceramic tiles have even worse conductivity, they are dielectrics. As the dielectrics have contact to or are in between conducting elements in a geometric relationship they form capacitors. This circuit consisting of capacitors and resistors permit AC current to flow. Aside from some other effects the current should be the same order of magnitude in both configurations.

What's the difference now between both cases? When touching the copper wire you form a conductive connection with a very small area for the carriers to pass. As two conductors connect, there can't be a strong electric field either. Due to the small area the current density maximises and you can sense it. n.b.: you can't sense it at your feet, can you?

The other case differs as you touch a dielectric. This dielectric differs from the surrounding air but not very much to change the electric field dramatically. Hence the electric field vectors connect to your skin perpendicular and with merely unchanged field strength. At your skin the electrical surface charge influenced by the field causes a current, but this time distributed over the surface of your hand. You can't sense it.

When a fault occurs in an un-earthed metal cased device the case becomes live. When you touch it you form a circuit. Now you'd think that current couldn't flow through solid wood, etc. Well, that would be the case for DC, but not for AC. You see, you form part of a capacitor. You're basically one plate of a capacitor, the ground being the other. The floor, your boots, etc, form the dielectric insulator between the two.

The capacitor would block any DC current, but it allows the AC to flow quite happily. The equivalent circuit would be:

^{simulate this circuit – Schematic created using CircuitLab}

The resistance of your body, and the resistance of the ground both limit the amount of current, but it only takes a tiny amount to kill you.

Now with the case grounded, and typically this involves a wire connecting the ground direct back to the ground point, which is also connected to neutral, and a fault occurs, the current will flow straight down the earth wire back to the neutral. This is a much much lower resistance connection than any human could provide, so considerably more current flows. This results in the fuse blowing isolating the circuit.

Also, if the fuse were not to blow for whatever reason (too high a rating?) the low resistance path would effectively short out the human reducing the current available to shock you to an absolutely minuscule amount.