Current, electrical root-mean-square

An electrical measuring instrument contains electrical circuits incorporating capacitance, inductance, and resistance. In the absence of resistance, a circuit tends to oscillate with a definite frequency /when disturbed. For optimum performance an amount of resistance is incorporated that is barely sufficient to damp the oscillations resulting from transient inputs the circuit is then said to be critically damped. For a critically damped circuit it can be shown that the root-mean-square (rms) fluctuations in voltage V and in current /are given by... 

In order to safeguard against electric shock at the far end of the cable, where the AC root mean square voltage may exceed 50 V, the earth loop impedance must be limited to a particular value. This value is such that the fault current should only be passed by the protective device at the supply for a specific period of time, i.e. to satisfy the /-squared- criterion given in sub-section 13.1.1. The correlation of loop impedance, current and time varies with the type of protective device, e.g. fuse. 

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