Question

A generator produces a voltage that is given by $ V=240\sin 120\,t $ volt, where t is in seconds. The frequency and $ \text{rms} $ voltage are

• A. 60 Hz and 240 V
• B. 19 Hz and 120 V
• C. 19 Hz and 170 V
• D. 754 Hz and 170 V

Answer 1

Answer: (C)

Voltage equation is
$V=240\, \sin 120\, t$
Comparing with $V=V_{0} \sin \omega t$, we get
$\omega =120$
and $V_{0} =240\, V$
$\therefore 2 \pi n =120$
or $n=\frac{120 \times 7}{2 \times 22}=19\, Hz$
and $V_{ rms } =\frac{V_{0}}{\sqrt{2}}=\frac{\sqrt{2} V_{0}}{2}$
$=\frac{\sqrt{2} \times 240}{2}=120 \sqrt{2}$
$\approx 170\, V$