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If the voltage in an ac circuit is repre...

If the voltage in an `ac` circuit is represented by the equation.
`V = 220 sqrt(2) sin (314 t - phi)` volt calculate (a) peak and rms value of the voltage, (b) average voltage, (c) frequency of `ac`.

Text Solution

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(a) As in case of `ac`,
`V = V_(0) sin (omega t - phi)` , The peak value
`V_(0) = 220 sqrt(2) = 311 V` and as in cas3 of `ac`.
`V_("rms") = (V_(0))/(sqrt(2)), V_("rms") = 220 V`, (b) In case of `ac`
`V_("rms") = (2)/(pi) V_(0) = (2)/(pi) xx 311 = 198.17 V`
(c ) As `omega = 2 pi f, 2 pi f = 314`
i.e., `f = (314)/(2 xx pi) = 50 Hz`
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Knowledge Check

  • If the voltage in an ac circuit is reparesented by the equation V=220 sqrt(2) sin (314 t - phi) , calculate average voltage

    A
    220 V
    B
    `622 // (pi V)`
    C
    `220//sqrt(2) V`
    D
    `200 sqrt(2) V`

  • If the voltage in an ac circuit is reparesented by the equation V=220 sqrt(2) sin (314 t - phi) , calculate frequency of ac

    A
    `50 Hz`
    B
    `50 sqrt(2) Hz`
    C
    `50//sqrt(2) Hz`
    D
    `75 Hz`

  • If the voltage in an ac circuit is reparesented by the equation V=220 sqrt(2) sin (314 t - phi) , calculate rms value of the voltage

    A
    220 V
    B
    314 V
    C
    `220 sqrt(2) V`
    D
    `200//sqrt(2) V`

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