Question

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.

Root-Mean-Square (R.M.S.) Value

The r.m.s. value of an alternating current h given by that steady (d.c.) current which when flowing through a given circuit for a given time produce the same heat as produced by the alternating current when flowing through the same circuit for the same time.

It is also known as the effective or virtual value of the alternating current the former term being used more extensively.

Form Factor

It is defined as the ratio

Kf = r.m.s value / average value = 0.707Im / 0.637 Im = 1.11 (for sinusoidal alternating currents only)

in the case of sinusoidal alternating voltage also

Kf = r.m.s value / average value = 0.707Em / 0.637 Em = 1.11

As is clear, the knowledge of form factor will enable the r.m.s. value to be found from the arithmetic mean value and vice versa.