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The input voltage $v(t)$ and current $i(t)$ of a converter are given by,

$\begin{array}{l} v(t)=300 \sin (\omega t) V \\ i(t)=10 \sin \left(\omega t-\frac{\pi}{6}\right)+2 \sin \left(3 \omega t+\frac{\pi}{6}\right)+\sin \left(5 \omega t+\frac{\pi}{2}\right) A \end{array}$

where, $\omega=2 \pi \times 50 \: \mathrm{rad} / \mathrm{s}$. The input power factor of the converter is closest to

  1. $0.845$
  2. $0.867$
  3. $0.887$
  4. $1.0$

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