Q107 / 120 · VITEEE 2010 · Physics

Using an AC voltmeter the potential difference in the electrical line in a house is read to be $234 \mathrm{~V}$. If line frequency is known to be 50 cycles/s, the equation for the line voltage is

  • A
    $\quad V=165 \sin (100 \pi t)$
  • Correct answer
    B
    $\quad V=331 \sin (100 \pi t)$
  • C
    $\quad V=220 \sin (100 \pi t)$
  • D
    $V=440 \sin (100 \pi \mathrm{t})$

Solution

$E=E_{0} \sin \omega t$ Voltmeter read rms value $\therefore E_{0}=\sqrt{2} \times 234 \mathrm{~V}=331 \mathrm{~V}$ and $\omega t=2 \pi n t=2 \pi \times 50 \times t=100 \pi t$ Thus, the equation of the line voltage $E=331 \sin (100 \pi t)$

Hence, the correct answer is option: 'B'.

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