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  • The voltage of an ac source varies with time according to the equation V = 100 sin(100t) cos(100<img alt="\pi" src="http

The voltage of an ac source varies with time according to the equation V = 100 sin(100\pit) cos(100\pit) where t is in seconds and V is in volts. Then

Option: 1

The peak voltage of the source is 100 volts


Option: 2

The peak voltage of the source is 50 volts


Option: 3

The peak voltage of the source is 100 / \sqrt{2}volts


Option: 4

The frequency of the source is 50 Hz


Answers (1)

best_answer

The given equation can be written as follows

\mathrm{V=50 \times 2 \sin 100 \pi t \cos 100 \pi t=50 \sin 2(100 \pi t)=50 \sin 200 \pi t \quad(\because \sin 2 \theta=2 \sin \theta \cos \theta)}

\mathrm{\text { Hence peak voltage } \mathrm{V}_0=50 \text { volt and frequency } \mathrm{v}=\frac{200 \pi}{2 \pi}=100 \mathrm{~Hz}}

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