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Homework Help: RLC circuit - total impedance,phasor analysis etc

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data
    A resistor, R = 100 Ω, an inductor, L = 0.20 H and a capacitor, C = 3 µF are connected in series across an ac source of VS = 100 V and frequency, f = 200 Hz. Calculate the following for this series circuit:
    a) the total circuit impedance (Zt)
    b) the total circuit current (IS)
    c) the voltage drop across each component (VR, VL and VC)
    d) the phase angle between VS and It.
    e) Draw the phasor diagram of voltages and current for the circuit.
    f) What is the frequency of the ac source for maximum current to flow?
    g) What is the quality factor, Q, of the circuit at the frequency calculated in part f)?



    2. Relevant equations

    in attachment

    3. The attempt at a solution
    attachment
    a) I think is right.
    b) Not sure about since i dont have vmax do I??
    c) really doubt is right but I cant think of another way to do it
    d) tan(phi)=X_L-X_C/R which I got -7.9 degrees????
    e) I'm trying to understand the phasor analysis paragraph in the text and all I know is that I will need VR,max,[tex]\epsilon[/tex]max and VC,max all of which I should be able to calculate when I know if my I from b) is right.. even when I have that Im still not sure how to draw it???
    f) and g) I am really stumped on....
    Thanks for any and all help.

    the d) I have in the pic is for another question-sorry I cant see how to remove that attachment.
     

    Attached Files:

  2. jcsd
  3. Sep 1, 2010 #2

    Andrew Mason

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    Homework Helper

    Assume the AC voltage is 100 V RMS. Vmax is V RMS/.707. But I am not sure why you need Vmax here. Use: I = V/Z
    The phasor sum of all the voltage drops adds (vectorally) to the applied voltage. Remember that voltage across the inductor is 180 degrees ahead of the voltage across the capacitor and the voltage across the resistor is perpendicular to that across the inductor and capacitor. So draw VR pointing along the +x axis, VL along the + y axis and VC along the -y axis. VR = IR. |VC| = IXC and |VL|= IXL
    Looks right.
    You don't actually need to use Vmax. Just use the given 100 VAC (rms) and add them using a phasor diagram.


    AM
     
    Last edited: Sep 1, 2010
  4. Sep 1, 2010 #3
    Thanks Andrew,
    for b I get the same answer, the reason I had Vmax is because the formula in my textbook says I = Vmax/Z but thats probably for Imax???
    Still confused about c) do I need to draw a diagram???? I used VR = IR. |VC| = IXC and |VL|= IXL so my numerical answers should be right????
    e) im still stumped on, how do i find the angle for V r max,E max,Vcmax or the magnitude?
    f) not sure--thinking that I should find I_max using Irms/swrt(2) but that will give me the max current flow at 200Hz won't it?? If im looking for max current flow I'm after the resonant frequency i think but I don't know any formula for that??
    g)Q=X_L/R=wL/R but since I dont know how to find the frequency I cant do this yet??
     
  5. Sep 2, 2010 #4

    Andrew Mason

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    Homework Helper

    That would be Imax, correct.
    Right. But according to Kirchoff's laws, the voltages must add up to the applied voltage. They do add up at any given moment but to do that you have to take into account the phase differences between the voltages. To do that, you use a phasor diagram.
    Draw a phasor diagram of the voltages. You don't need to use Vmax. You can use Vrms. Draw the voltage vectors as I suggested in my last post using the values you found in c). Then draw a phasor showing the current vectors. The lengths will be proportional to voltages but the phase angles of the inductor and capacitor currents will have different directions.
    Use I = V/Z. In order to maximize I, you need to minimize Z. How do you do that? (hint: express XL and XC in terms of f, L and C.)
    Find f and you will have no problem.

    AM
     
  6. Sep 7, 2010 #5
    Hey Andrew,
    been a while but I finally got around to finishing this problem.
    I'm really not sure about my phasor diagram, I ended up using Vmax just because I had it worked out from a previous question. my Vcmax is way bigger than both my V_r,max and emf max - not sure if this means its wrong or not???
    for f) I got 205.5Hz and for g I got 2.58, sound right??? also what are the units for quality factor?

    Thanks
     

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