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LRC circuit

  1. May 6, 2015 #1
    problem 4.png


    2. Relevant equations
    XL = ωL
    XC = 1/ωC
    Z= sqrt(R^2+(XL-XC)^2)
    ∅ = tan^-1(XL-XC/R)

    3. The attempt at a solution

    A) a)
    Irms = Vrms/R = 100 V/400 Ω = .25 A
    b) 1) V= Vrms =100 V
    2) V = IrmsXL = IrmsωL = (.25)(1000)(.9) = 225 V
    3) V= IrmsXC = Irms/ωC = (.25)/((1000)(2E-6)) = 125 V
    4) this part I am not sure how to do.
    5) V = IrmsZ = Irmssqrt(R^2+(XL-XC)^2) = (.25)sqrt(400^2 + (900 - 500)^2) = 141 V

    c) ∅=tan^-1(XL-XC/R) = tan^-1(400/400) = 45°
    it is positive so voltage leads

    B) a) ω = 1/sqrt(LC) = 1/sqrt(.9(2E-6)) = 745 rad/sec
    b) 1) still 100 V
    2) V = IrmsXL = IrmsωL = (.25)(745)(.9) = 168 V
    3) V = IrmsXC = Irms/ωC = (.25)/((745)(2E-6)) = 168 V
    4) ???
    5) V = IrmsZ = IrmsR = .25(400) = 100 V


    I am not entirely confident I did all of these right. feedback would be greatly appreciated
     
  2. jcsd
  3. May 6, 2015 #2

    donpacino

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    your part a is wrong. I=V/Z, with Z being the impedance of the circuit. Since it is an AC waveform, the inductor and capacitor will have some impedance
     
  4. May 6, 2015 #3
    so part a) would be I = V/Z = V/ sqrt(R^2 + (XL-XC)^2) = 100/sqrt(400^2 +(1000(.9-2E-6))^2) = .1 A ???

    also would I be able to do part 4 using the formula V = IZ where the R in the formula for Z is set to 0?
     
  5. May 6, 2015 #4

    donpacino

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    No.

    What have you learned about AC circuits and inductors and capacitors?
    Have you learned about the laplace transform yet?
     
  6. May 6, 2015 #5
    I haven't heard of the laplace transform. Both of the things I said are wrong? I am still wrong about part a) ?
     
  7. May 6, 2015 #6

    donpacino

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    the resistance at any given frequency for these purposes can be seen below
    inducotor: w*L
    capacitor: 1/(w*L)

    now the inductor, capacitor,and resistor.... are they in series or parallel?
     
  8. May 6, 2015 #7

    donpacino

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  9. May 6, 2015 #8
    they are in series
     
  10. May 6, 2015 #9

    donpacino

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    yup, so to find the total impedance, you add them together
     
  11. May 6, 2015 #10
    I = V/Z = V/ sqrt(R^2 + (XL+XC)^2)
    ???
    so when they are in parallel it is
    1/XL + 1/XC ??

    My book says XL-XC where does this come from?
     
  12. May 6, 2015 #11

    donpacino

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    somehow I missed your equations page. oops

    I forgot you havent really learned that much about AC so they gave you the equations.

    http://en.wikipedia.org/wiki/Complex_plane

    There are two ways to express complex numbers, polar and rectangular notation.
    sqrt(R^2 + (XL+XC)^2) essentially converts the rectangular notation to the magnitude of polar notation
    and ∅ = tan^-1(XL-XC/R) converts it to the angle of polar notation
     
  13. May 6, 2015 #12

    donpacino

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    in that case, the second answer you gave is correct
     
  14. May 6, 2015 #13
    the .1 A is correct for part a) ?

    For part 4) is this a case where the Voltage oscillates?
     
  15. May 6, 2015 #14

    donpacino

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    yes
    do you mean finding the phase angle??
    if yes then look at your equation for theta
     
  16. May 7, 2015 #15
    I mean to find the voltage across the LC part of the circuit (If I am understanding the question correctly)
    Originally I was thinking of using the equation for Z with R = 0 or
    Z = sqrt((XL-XC)^2)
    and then using
    V = IZ
     
  17. May 7, 2015 #16
    I am still trying to figure this out. Is this one of the cases where I have to use the formula for oscillating voltage? V=v0coswt ?
     
  18. May 11, 2015 #17

    donpacino

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    recall each part has an impedance. you know what the impedance is

    V=I*Z
     
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