Answer to Question #142975 in Electricity and Magnetism for Elian

Question

Write down the equation for a sinusoidal voltage of 50 Hz and its peak value is 20 V. Draw the corresponding voltage versus time graph.

Answer 1

According to https://en.wikipedia.org/wiki/Alternating_current#Mathematics_of_AC_voltages

$V(t) = V_{\text{peak}}\sin(\omega t) = V_{\text{peak}}\sin(2\pi\nu t) = 20\sin(2\pi\cdot50 t) = 20\sin(100\pi\cdot t).$

The graph represents only two tenth of second, so we see only 5 oscillations of 50 per second (50 Hz)