the problems asks, the output voltage of an AC generator is givenby v=400 V sin
ID: 1745357 • Letter: T
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 sRelated Questions
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