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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) For ac voltage ,
V = `V_(0) sin (omegat-phi)`
The peak value of voltage `V_(0)=220sqrt(2)=311 V `
The rms value of voltage
`V_("rms")=(V_(0))/(sqrt(2)), V_("rms") = 220 V`
(b) Average voltage in full cycle is zero. Average voltage in half cycle is
`V_("avg")= (2)/(pi)V_(0)=(2)/(pi)xx311 = 198.17 V`
(c ) As `omega = 2pif, 2pif= 314 `
i.e, `f= (314)/(2xxpi) = 50 Hz`
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