Question

The voltage of an AC supply varies with time$\left(t\right)$ as $V=60\sin 50\pi t.\cos 50\pi t$. The maximum voltage and frequency are respectively (where $V$ is in $volt$ and $t$ is in $second$)

• A. $30$ $Volt$, $100$ $H_z$
• B. $60$ $Volt$, $50$ $H_z$
• C. $60$ $Volt$, $100$ $H_z$
• D. $30$ $Volt$, $50$ $H_z$

Answer 1

The correct option is D $30$ $Volt$, $50$ $H_z$

$V=60\sin 50\pi t\cos 50\pi t$

By rearranging

$V=2\times 30\sin 50\pi t\cos 50\pi t$

$2\sin \theta \cos \theta =\sin 2\theta$

$V=30\sin 100\pi t$

$V_{max}=30$ $V$,

$\omega =100\pi$

$\Rightarrow f=50$ $H_z$