Question

write mathematical expression for a 50HZ sinusoidal voltage of peak value 80v sketch the waveform versus time t​

Answer 1

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