Question
Download Solution PDFSine Wave RMS = ________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFParameters of sine wave
1.) Average value
The average of all the instantaneous values of an alternating voltage and current over one complete cycle is known as an average value.
\(V_{avg}={2V_m\over \pi}\)
\(V_{avg}=0.637V_m\)
The average value of the sine wave is 0.637 times the peak value.
2.) RMS value
The ‘RMS Value’ stands for Root Mean Squared value.
The RMS value of an alternating current is given by that steady (D.C) current which when flowing through a given time produces the same amount of heat as produced by the A.C when flowing through the same circuit for the same time.
\(V_{RMS}={V_m\over \sqrt{2}}\)
\(V_{RMS}=0.707V_m\)
The RMS value of the sine wave is 0.707 times the peak value.
3.) Form factor
The ratio of the RMS value to the average value is known as the form factor.
\(FF={V_{RMS}\over V_{avg}}\)
\(FF={0.707V_{m}\over 0.637V_{m}}\)
FF = 1.11
4.) Crest factor
The ratio of the maximum value (peak value) to the RMS value is known as the peak factor or crest factor.
\(CF={V_{p}\over V_{RMS}}\)
\(CF={V_{m}\over 0.707V_{m}}\)
CF = 1.414
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