QuestionDetails: (a) the resonance frequency W (b) one-half the resonance freque

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QuestionDetails: (a) the resonance frequency
W
(b) one-half the resonance frequency
W
(c) one-fourth the resonance frequency
W
(d) two times the resonance frequency
W
(e) four times the resonance frequency
W the help on the same problem before hand is notworking in my calculations. please help!! QuestionDetails: A series circuit contains a 3.00 Hinductor, a 2.80 µF capacitor, and a 20.0 resistorconnected to a 120 V (rms) source of variable frequency. Find thepower delivered to the circuit when the frequency of the source iseach of the following. (a) the resonance frequency
W
(b) one-half the resonance frequency
W
(c) one-fourth the resonance frequency
W
(d) two times the resonance frequency
W
(e) four times the resonance frequency
W the help on the same problem before hand is notworking in my calculations. please help!!

Explanation / Answer

   we are given with
   C = 2.80 F
   R = 20.0
   L = 3.00 H
   Vrms = 120 V
   the resonant frequency is given by
   o = 2 fo
         = 1 / (LC)
   the inductive reactance is given by
   XL = L
   the capacitive reactance is given by
   XC = 1 / C
(a)
   at the resonance
   XC = XL
         =o L
         = (1 / (LC)) L
         = (L /C)
         = .......
   the impedence will be
   Z = (R2 + 0)
      = R
   Irms = Vrms / Z
          = .......amps
   the average power will be
   Pavg = Irms2 R
           = ....... W
(b)
   at = (1 / 2) o
   XL = (1 / 2) (XL)
         = .......
   Z = [R2 + (XL -XC)2]
       = .........
   Irms = Vrms / Z
          = .......amps
   the average power will be
   Pavg = Irms2 R
           = ....... W
(c)
   in the similar manner calculate for
   = (1 / 4) o (d)     = (2) o (e)    = (4) o

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