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What is the earth fault impedance?

Earth fault loop impedance is the path followed by fault current when a low impedance fault occurs between the phase conductor and earth, i.e. “earth fault loop”. Fault current is driven round the loop by the supply voltage. The higher the impedance, the lower the fault current will be and the longer it will take for the circuit protection to operate. So in short it is the impedance of the earth fault current loop starting and ending at the point of earth fault. This impedance is abbreviated to Zs. 

The earth fault loop impedance can be used with the supply voltage to calculate the earth-fault current, and hence, to properly determine earth cable size. 
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