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# The frequency of voltage for an AC circuit, the equation of alternating voltage is $V = 200\sin 314t$ is?A. 50HzB. 55HzC. 60HzD. 65Hz

Last updated date: 17th Jun 2024
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Hint We will derive the equation of alternating voltage then we will compare it with the given equation and will find the value of angular frequency. After getting angular frequency we will get the frequency by using the formula $\omega = 2\pi f$ .

Complete step-by-step solution
Alternating Voltage is that voltage whose magnitude changes with time and its direction is reversed periodically.
$e = - \dfrac{{d\phi }}{{dt}}$ , where $\phi$ = flux by magnetic field
e = instantaneous voltage
$e = - \dfrac{{d(\overrightarrow B .\overrightarrow A )}}{{dt}}$ , B= magnetic field and A= area
$e = - \dfrac{{d(BA\cos \theta )}}{{dt}}$ , $\omega = \dfrac{\theta }{t}$
$e = - BA\dfrac{{d(\cos (\omega t))}}{{dt}}$ , $e = BA\omega \sin (\omega t)$
$e = {e_ \circ }\sin (\omega t)$ , ${e_ \circ }$ = peak voltage
Now compare this equation with $V = 200\sin 314t$
$\omega = 314{s^{ - 1}}$
$\omega = \dfrac{{2\pi }}{T}$ , T= time period
$\omega = 2\pi f$ , f= frequency of the voltage
$f = \dfrac{\omega }{{2\pi }} = \dfrac{{314}}{{2\pi }}$
$f = 50Hz$

Option(A) 50Hz