Q82 / 90 · KVPY 2011 (SB/SX) · Physics

For a domestic AC supply of $220 \mathrm{~V}$ at 50 cycles per second, the potential difference between the terminals of a two pin electric outlet in a room is given by -

  • Correct answer
    A
    $V(t)=220 \sqrt{2} \cos (100 \pi t)$
  • B
    $\mathrm{V}(\mathrm{t})=220 \cos (50 \mathrm{t})$
  • C
    $\mathrm{V}(\mathrm{t})=220 \cos (100 \pi \mathrm{t})$
  • D
    $V(t)=220 \sqrt{2} \cos (50 \mathrm{t})$

Solution

R.M.S. value $=220 \mathrm{~V}$ Peak value $=220 \sqrt{2}$ $\omega=2 \pi \mathrm{n}$ $=2 \pi \times 50$ $=100 \pi$ $V(t)=220 \sqrt{2} \cos (100 \pi t)$

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

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