Question

The equation of an a.c voltage is $V=100\sqrt{2}\sin \left(100\pi t\right)$. Find the rms value and the frequency of the voltage.

Answer 1

For ac voltage,

$V_{rms}=0.707\times V_m$

$\omega =2\pi f$

The general expression for sinusoidal waveform is given by,

$V_t=V_{m}sin\left(\omega t\right)=\frac{V_{rms}}{0.707}sin\left(2\pi ft\right)$

comparing the given equation with general expression we get,

$V_{rms}=0.707\times 100\sqrt{2}=100volt=100V$

$f=\frac{100\pi }{2\pi }=50Hz$