write mathematical expression for a 50HZ sinusoidal voltage of peak value 80v sketch the waveform versus time t
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Explanation:
Given data
frequency(f)=50 Hz
peak value of voltage(V0)=20 Volt
Angular frequency of sinusoidal voltage wave
\omega =2 \pi fω=2πf
\implies \omega=2\pi\times50=100\pi⟹ω=2π×50=100π rad/sec
standard sinusoidal form of voltage is given by
V=V_{0}\sin\omega tV=V
0
sinωt
putting value of V0 and \omegaω then
{V=20\sin100\pi t}V=20sin100πt
time period for one cycle is given by
T=\frac{1}{f}= \frac{2\pi}{\omega}T=
f
1
=
ω
2π
Now T=\frac{1}{50}=0.02 secT=
50
1
=0.02sec
therefore sinusoidal voltage form is V=V_{0}\sin100\pi tV=V
0
sin100πt and time period for one cycle T=0.02 secT=0.02sec.
\implies⟹ voltage versus time graph is below
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