Question

The relationship between A.C voltage and time in SI unit is $V=120\sin \left(100\pi T\right)\cos \left(100\pi t\right)$ volt value of peak voltage and frequency will be :

• A. $120$ volt and $100Hz$
• B. $\frac{120}{\sqrt{2}}$ volt and 100 Hz
• C. $60$ volt and $200Hz$
• D. $60$ volt and $100Hz$

Answer 1

The correct option is D $60$ volt and $100Hz$

$V=120\sin \left(100\pi T\right)\cos \left(100\pi J\right)$

$V=\frac{1}{2}\times 120\times 2\sin \left(100\pi T\right)\cos \left(100\pi J\right)$

$V=60\sin (2\times 100\pi T)$

$V=60\sin \left(200\pi T\right)$

Comparing with $V=V_m\sin \omega J$

$V_m=60Volt$

$\omega T=200\pi T$

$2\pi f=200\pi$

$f=\frac{200}{2}$

$f=100HZ$