**Important
values of Alternating Quantities**

**1) Peak Value\(\left(
{{i}_{0}}\,or\ {{V}_{0}} \right)\): **The
maximum value of alternating quantity (i or V) is defined as peak value or
amplitude.

**2) Mean square value\(\left( \overline{{{V}^{2}}}\,or\,\overline{\,{{i}^{2}}} \right)\): **The average of square of instantaneous values in one cycle is called mean square value. It is always positive for one complete cycle. E.g. \(\overline{{{V}^{2}}}=\frac{1}{T}\int\limits_{0}^{T}{{{V}^{2}}dt}=\frac{{{V}_{0}}^{2}}{2}\) (or) \(\overline{{{i}_{0}}^{2}}=\frac{{{i}_{0}}^{2}}{2}\).

**3) Root mean square value: **Root of mean of square of voltage or current
in an ac circuit for one complete cycle is called root mean square value. It is
denoted by \({{V}_{rms}}\) (or)\({{i}_{rms}}\)
.

\({{i}_{rms}}=\sqrt{\frac{{{i}_{1}}^{2}+{{i}_{2}}^{2}+……}{n}}=\sqrt{\overline{{{i}^{2}}}}=\sqrt{\frac{\int\limits_{0}^{T}{{{i}^{2}}dt}}{\int\limits_{0}^{T}{dt}}}=\frac{{{i}_{0}}}{\sqrt{2}}=0.707{{i}_{0}}=70.7%{{i}_{0}}\) Similarly,

\({{V}_{rms}}=\frac{{{V}_{0}}}{\sqrt{2}}=0.707{{V}_{0}}=70.7%\,of\,{{V}_{0}}\)r.m.s value of ac is equal to that value of dc, which when passed through a resistance for a given time will produce the same amount of heat as produced by the alternating current when passed through the same resistance for same time.

**4) Mean of Average value\(\left( {{i}_{avg}}\,or\,{{V}_{avg}}\, \right)\): **The average value of alternating quantity for one complete cycle is zero. The average value of ac over half cycle\(\left( t=0\,\,to\,\,\frac{T}{2} \right)\)\({{i}_{avg}}=\frac{\int_{0}^{T/2}{i\,dt}}{\int_{0}^{T/2}{dt}}=\frac{2{{i}_{0}}}{\pi }=0.637{{i}_{0}}=63.7%\,\,of\,{{i}_{0}}\,\) similarly, \({{V}_{avg}}=\frac{2{{V}_{0}}}{\pi }=0.637{{V}_{0}}=63.7%\,\,of\,\,{{V}_{0}}\).

**5) Peak to Peak value: **It is equal to the sum of the magnitudes of positive and negative peak values. Therefore, Peak to peak value = \({{V}_{0}}+{{V}_{0}}=2{{V}_{0}}=2\sqrt{2}{{V}_{rms}}=2.828{{V}_{rms}}\).

**6) Form factor and Peak factor: **The ratio of r.m.s value of ac to its average
during half cycle is defined as form factor. The ratio of peak value and r.m.s
value is called peak factor.