the problems asks, the output voltage of an AC generator is givenby v=400 V sin

Question

the problems asks, the output voltage of an AC generator is givenby v=400 V sin (90t). the generator is connected acrossa 1.1 H inductor. find the following?

a. frequency of the generator. ( answer is 45 Hz)

b. rms voltage across the inductor ( answer is 283 V)

c. inductive reactance (answer is 311 )

d. rms current in the inductor ( .91A)

e. maximum current in the inductor? (1.28A)

f. average power delivered to the inductor =?W

g. find an expression for the instantaneous current ( use thefollowing variables as necessary: t, pi.)

h. at what time after t = 0 does the instantaneous current firstreach 1.00 A? (use the inverse sine function)

can someone please help me with problems F-H? thank you. willrate highly!!

Explanation / Answer

The output voltage of an AC generator is given by V=400V sin (90t). Inductance (L) = 1.1 H Compare this equation with V =Vmaxsint a) Then = 90        2f = 90           f = 45Hz b) Given that Vmax = 400V                   Vrms= Vmax / 2                          = (400V) / 2                          = 283 V c) Formula for the inductive reactance is  XL = 2fL                                                                  =2(3.14)(45Hz)(1.1H) = 311 d) rms current is Irms = Vrms /XL                             = (283V) / (311)                             = 0.91A e) Max current is Imax =Irms(2)                               = (0.91A)(2)                               = 1.28 A f) verage power is P = VrmsIrms                             = (283V)(0.91A) = 257.53 W g) Instantaneous current is I = Imaxsint= (1.28A)sin(90t) h) Given that 1.0 A = (1.28A)sin(90t)                     0.78125 =sin90t                        90t = sin-1(0.78125) = 51.4                              t = 0.1817 s                             = (283V)(0.91A) = 257.53 W g) Instantaneous current is I = Imaxsint= (1.28A)sin(90t) h) Given that 1.0 A = (1.28A)sin(90t)                     0.78125 =sin90t                        90t = sin-1(0.78125) = 51.4                              t = 0.1817 s

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