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Calculating values of impedance in a series/parallel circuit

  1. Sep 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Hello everyone, I have recently come under some stress from not being able to get these answers correct. I need to calculate these values:


    1. Zeq
    2. IT
    3. XL2
    4. XL1
    5. VR1
    6. VR2
    7. VL1
    8. VL2
    For this series circuit:


    upload_2015-9-14_10-20-4.png

    And these values:


    1. Zeq
    2. IT
    3. XL2
    4. XL1
    5. IR1
    6. IR2
    7. IL1
    8. IL2
    For this parallel circuit:

    upload_2015-9-14_10-21-24.png

    2. Relevant equations
    I have been using these equations, but I am told that they are incorrect. My professor will not indicate what the correct equations are and I cannot find them in my textbook or online. Any help would be appreciated.

    Zeq = sqrt(RT^2+XL^2) where XL is both values of XL1 and XL2 added together.
    IT = Vs/ZT This is where I get confused, is ZT the same as Zeq?
    XL2 = (2*pi*Frequency*L2)
    XL1 = (2*pi*Frequency*L1)
    VR1 = (R1/RT)*Vs
    VR2 = (R2/RT)*Vs
    VL1 = (L1/LT)*Vs Where LT is L1 and L2 added together.
    VL2= (L2/LT)*Vs
    IR1= I could not find the equation for this value.
    IR2 = I could not find the equation for this value.
    IL1 = Vs/L1
    IL2 = Vs/L2
    3. The attempt at a solution
    Here are the values that I came up with for the series circuit:

    Phase = -tan((942.48+502.65)/100) = 86.04 degrees.
    a. Zeq = 15Vrms / .03333A = 450ohms
    b, It = 15Vrms/450ohms = 33.33mA∠-86.04 degrees
    c. XL1 = (2*pi*1000Hz*.150H) = 942.48ohms
    d. XL2 = (2*pi*1000Hz*.08) = 502.65ohms
    e. VR1 = 150ohms/450ohms * 15Vrms = 5Vrms ∠0 degrees
    f. VR2 = 300ohms/450ohms * 15Vrms = 10Vrms ∠0 degrees
    g. VL1 = .08H/.23H * 15Vrms = 5.22Vrms ∠-90 degrees
    h. VL2 = .150/.23H * 15Vrms = 9.78Vrms ∠-90 degrees


    And here are the values I came up with for the parallel circuit:


    a. Zeq = 15Vrms / .03333 = 450ohms
    b. IT = 33.33mA ∠-86.04 degrees
    c. XL2 = (2*pi*1000Hz*.150H) = 942.48ohms
    d. XL1 = (2*pi*1000Hz*.08H) = 502.65ohms
    e. VR1 = 150ohms/450ohms * 15Vrms = 5Vrms ∠0 degrees
    f. VR2 = 300ohms/450ohms * 15Vrms = 10Vrms ∠0 degrees
    g. IL1 = 15Vrms/.08H = 187.5A.
    h. IL2 = 15Vrms/.150H = 100A

    Any help at all would be very, very much appreciated. I really cannot find the equations for the life of me, and it is frustrating.
     
  2. jcsd
  3. Sep 14, 2015 #2

    Hesch

    User Avatar
    Gold Member

    That's correct as for the absolute value of Zeq, ( | Zeq | ).

    Are you not familiar with complex impedances ? Here is the value:

    Zeq = ( R1+R2 ) + jω( L1+L2 )

    You can calculate exactly like if all the impedances were ohmic, just using complex values instead of real values.

    It will be much more easy ( your calculator will do the job ) to calculate voltages, current, phases, etc. using complex values:

    As for the series connection, IR1 = IR2 = IL1 = IL2 = Vs / Zeq ( like I = V / R ).
     
  4. Sep 14, 2015 #3
    Thank you very much for the reply! I am not familiar with complex impedances. In Zeq = (R1+R2) + jω(L1+L2), what values are "j" and "ω"? So IR1, IR2, IL1 and IL2 are all calculated by Vs/Zeq?
     
  5. Sep 14, 2015 #4

    Hesch

    User Avatar
    Gold Member

    j ( also called "i" ) is the imaginary operator: j2 = -1.
    ω is the angular velocity in radians/sek. ( ω = 2πf ).
    Yes, through all components in series, the currents are identical ( Kirchhoffs 1. law, KCL ).

    I'm sorry, I thought that the complex values of impedances was what your professor meant. But you will learn about these complex impedances. I promise.
     
  6. Sep 15, 2015 #5
    Alright, everything makes much more sense now. Thank you very much for your help, I truly appreciate it!
     
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