In a series resistor-inductor (R-L) circuit, closing the switch at the start of the time period simulates a three-phase short circuit, a fault condition where all three phases of an unloaded synchronous machine are short-circuited. When there is no fault impedance and no initial current, the initial voltage is determined by the phase angle of the source voltage.

Using Kirchhoff's Voltage Law (KVL) to analyze this circuit helps determine the total asymmetrical fault current, which consists of two main components. The AC fault current, also known as the symmetrical or steady-state fault current, follows a sinusoidal pattern. On the other hand, the DC offset current decreases exponentially over time, with its rate of decay defined by the ratio of inductance to resistance. The magnitude of the DC offset varies with the source angle, peaking at a specific phase angle of the source.

The calculation of the RMS asymmetrical fault current, including the maximum DC offset, involves expressing the time constant and time in terms of cycles and frequency. This RMS asymmetrical current is found by multiplying the RMS AC fault current by an asymmetry factor. The asymmetry factor reflects the influence of the DC offset current. As the time constant increases, the RMS current decreases, which demonstrates the effect of the inductance-to-resistance ratio on the current. Higher ratios of reactance to resistance result in higher RMS current values.

This analysis is essential for understanding fault conditions in electrical circuits and designing systems to handle such events. By considering the different components of fault current and their dependency on circuit parameters, engineers can better predict and mitigate the effects of faults in electrical systems. This knowledge is critical for ensuring the reliability and safety of power systems.