The voltage of an ac supply varies with time | vedclass

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Question

(D) Given the voltage equation: $V = 120 \sin(100\pi t) \cos(100\pi t)$.Using the trigonometric identity $\sin(2	heta) = 2 \sin 	heta \cos 	heta$,w

Vedclass · Accepted Answer

$60 \, V, 100 \, Hz$

Vedclass · Answer

(D) Given the voltage equation: $V = 120 \sin(100\pi t) \cos(100\pi t)$.Using the trigonometric identity $\sin(2	heta) = 2 \sin 	heta \cos 	heta$,we can rewrite the equation as:$V = 60 	imes (2 \sin(100\pi t) \cos(100\pi t))$$V = 60 \sin(200\pi t)$.Comparing this with the standard form $V = V_{\max} \sin(\omega t)$,we get:Maximum voltage $V_{\max} = 60 \, V$.Angular frequency $\omega = 200\pi \, rad/s$.Since $\omega = 2\pi 
u$,the frequency $
u$ is:$
u = \frac{\omega}{2\pi} = \frac{200\pi}{2\pi} = 100 \, Hz$.Thus,the maximum voltage is $60 \, V$ and the frequency is $100 \, Hz$.

The voltage of an $ac$ supply varies with time $(t)$ as $V = 120\sin(100\pi t)\cos(100\pi t)$. The maximum voltage and frequency respectively are:

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