Question

(a) Explain the significance of the root-mean-square value of an alternating current or voltage waveform. Define the form factor of such a wave form.

(b) Two 10 MVA 3 phase Alternator operate in parallel to supply at 0.8 power factor with lagging load of 15 MVA. If the output of one Alternator is 8 MVA at 0.9 lagging.

(i) Calculate the output of second Alternator.

(ii) Calculate the value of Power factor of second Alternator.

Answer 1

Part (a)

The root-mean-square (RMS) value of an alternating current (AC) or voltage waveform represents the equivalent DC value that would produce the same heating effect in a resistive load. In simpler terms, it's the effective value of the varying AC signal. For a sinusoidal waveform, the RMS value is 0.707 times the maximum (peak) value (Irms = 0.707 * Imax or Irms = Imax / √2). Ammeters and voltmeters typically measure the RMS value of current and voltage, respectively. Unless otherwise stated, values of AC current and voltage are assumed to be RMS values in electrical engineering.

The form factor of an AC waveform is the ratio of its RMS value to its average value. For a perfect sine wave, the form factor is approximately 1.11 (RMS value/Average Value = 1.11). This factor indicates how closely a waveform resembles a pure sine wave; a form factor closer to 1.11 suggests a waveform that is more sinusoidal.

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