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if voltage in ac circuit is …

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if voltage in ac circuit is 220√2sin(314t-q)calculate peak and rms voltage average voltage over half cycle frequency of ac
  • 1 answers

Sia ? 6 years, 6 months ago

  1. For a.c. voltage
    {tex}V = {V_0}\;\sin \left( {\omega t - \phi } \right){/tex}
    The peak value
    {tex}{V_0} = 220\sqrt 2 = 311V{/tex}
    The rms value of voltage
    {tex}{V_{rms}} = \frac{{{V_0}}}{{\sqrt 2 }};\;{V_{rms}} = 220V{/tex}
  2. Average voltage in full cycle is zero. Average voltage in half cycle is
    {tex}{V_{av}} = \frac{2}{\pi }{V_0} = \frac{2}{\pi } \times 311 = 198.17V{/tex} = 198.17 V
  3. As {tex}\omega = 2\pi f,\;2\pi f = 314{/tex}
    i.e. {tex}f = \frac{{314}}{{2 \times \pi }} = 50\;Hz{/tex} = 50 Hz
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