Question

If a circuit has 50 Hz frequency and its peak value is 20V. Calculate the sinusoidal voltage. Also calculate the time for one cycle and draw the corresponding voltage versus time graph.

Answer 1

Given data

frequency(f)=50 Hz

peak value of voltage(V₀)=20 Volt

Angular frequency of sinusoidal voltage wave

$\omega =2 \pi f$

$\implies \omega=2\pi\times50=100\pi$ rad/sec

standard sinusoidal form of voltage is given by

$V=V_{0}\sin\omega t$

putting value of V₀ and $\omega$ then

${V=20\sin100\pi t}$

time period for one cycle is given by

$T=\frac{1}{f}= \frac{2\pi}{\omega}$

Now $T=\frac{1}{50}=0.02 sec$

therefore sinusoidal voltage form is $V=V_{0}\sin100\pi t$ and time period for one cycle $T=0.02 sec$.

$\implies$ voltage versus time graph is below