Current through protective earthing
If you know the resistance of the short path from the power panel live back to the grounding point, you simply use Ohm's Law to figure out the current. 

\$Current = Voltage/Resistance\$

How much that resistance is depends on where the short is.

Consider the two examples below.







simulate this circuit &ndash; Schematic created using CircuitLab

In the left lamp the short is direct from the live line to earth, there is no resistance in the short circuit other than the wiring, and so current will be large.

10A on a direct live line short is actually very small. Hundreds, or even thousands of amps would be typical for a direct short from live to ground till the breaker or fuse goes.

In the right lamp the short is downstream from the lamp, as such the short circuit current will be whatever the lamp would take normally with the switch closed. Note, also in the right circuit, when the switch IS closed, some of the return current flows back through the neutral line and some through the short path to ground.

Notice in the right circuit, when the switch is in either state, the short circuit would NOT trip a classical breaker or blow a fuse since the current is no greater than the regular load. As such, a regular circuit breaker or fuse does not protect individuals from being electrocuted with this kind of short.

This is why modern standards require the use of earth leakage circuit breakers (ELCB), also known as ground fault interrupters (GFI). These devices effectively monitor and compare the current going out the live wire against the current returning via the neutral wire. If there is a difference, current has leaked to earth, (or somewhere else), and the breaker trips and cuts the power.  



Looking at the typical ELCB circuit above, you can see that the live wire and neutral wire are wrapped round a toroid on their way to the load. When there is no leakage, the coils cancel each other out and no net magnetic field is generated in the toroid. If there is an imbalance in currents a field is generated that creates a current in the search coil that trips the relay.

The current imbalance required to trip these devices is very small in the low milliamps range. However, be aware, that does not mean there can not be a short burst of high current, Amps. If that short path is through you, and your heart, that can still be capable of seriously hurting you.