A sinusoidal signal as show in the figure can be represented by,
f(t)=A sinwt ; Where A is peak amplitude and w is angular frequency in radians/second
Sinusoidal signal is a periodic signal with time period T and frequency f which denotes number of cycles of signal that took place in a second.
[tex]w = 2\pi f[/tex] where f is frequency in herzt. The time period [tex]T = \frac{{2\pi }}{w} = \frac{1}{f}[/tex]
Higher the frequency smaller the time period.
The angle [tex]\theta [/tex] is called the phase angle of sinusoid.
Consider a sine function, [tex]v(t) = {V_m}\sin \omega t[/tex]
Then average value of v(t) =[tex]\frac{{{V_m}}}{T}\int\limits_0^T {\sin \omega tdt = \frac{{{V_m}}}{T}} \mathop {\left[ {\frac{{\cos \omega t}}{\omega }} \right]}\nolimits_0^T = 0[/tex]
Thus, the average value of sine wave is zero.
The rms value of the sine wave is, [tex]{V_{rms}} = \frac{1}{{2\pi }}\int\limits_0^{2\pi } {\mathop {{V_m}}\nolimits^2 } \mathop {\sin }\nolimits^2 (\omega t)d(\omega t) = \frac{{{V_m}}}{{\sqrt 2 }}[/tex]
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