Answers for Assignment 12

w will be used for omega throughout.

58. Let |Ztot| = sqrt[ R2 + (wL-/1wC)2] which is the total impedance of the circuit. Then

(a) I = V0 / |Z| 


(b)         w L V0
     VL   = ------- 
            |Ztot|

            V0 R
     VR  = -----  
            |Ztot|
 

               V0 
     VC  = --------- 
            w C |Ztot|

            V0  |wL - 1/wC|
     VLC  = -------------------- 
                  |Ztot|
          VRLC = V0

(c) PL=0
     PC=0
     PR=R V02 / |Ztot|2

59.

     (a) Proof; tan(phi) = 1 / (wRC)

     (b) 

              1
   w1/2 = -----------
         sqrt(3) R C

     (c) Sketch (omitted)

60. Proof.

61.

     IC = 0.088 amp (E0/volt)

     IR = 0.083 amp (E0/volt)

     IL = 0.028 amp (E0/volt)

62.

     IR1 = 0.071 amp (V /volt)

     IR2 = 0.020 amp (V /volt)

     IR3 = 0.003 amp (V /volt)

     IL = 0.023 amp (V /volt)

     IC = 0.073 amp (V /volt)

     Itot = 0.077 amp (V /volt)

Last revised 1998/05/11