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posted by  tw79 on 11/6/2009 7:00:53 PM  |  status: Closed  |  Earned Karma: 30

AC Circuit

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N/A N/A N/A N/A 11/8/2009 at 6:00:00 PM
Question Details:

A series RLC circuit has an AC generator with frequency f = 76 Hz and amplitude Erms = 134 V. The current leads the generator voltage by 37° and the current in the circuit is Irms = 8 A.

Calculate the inductance of the circuit, given C = 69 µF.
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posted by esther_jyothi on 11/6/2009 7:59:38 PM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
Given
   Frequency  f = 76 Hz
                   Vrms  = 134 V
                     φ = 37 o
                     I rms = 8 A
                     C   =  69 μF
  we know that 
            tan φ  = XL - XC  / R
             Z  = Vrms / I rms
                  = 134  / 8
                   = 16.75Ω
             cos φ = R  / Z
                 R  = Z cos φ
                       = 16.75 x cos 37
                       = 13.3771 Ω
       so R tan φ =  XL - XC
           13.3771 x tan 37o  =   XL - XC
                  XL - XC   = 10
                   XL = 10 + XC
                   2πfL = 10 + (1 / 2π f C)
                            = 10 + (1 / 2 x 3.14x 76 x 65 x10-6 )
                         L     =  0.103 H
                 
          
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