RLC at resonance

Discussion in 'Homework Help' started by JoyAm, Sep 4, 2014.

  1. JoyAm

    Thread Starter Member

    Aug 21, 2014
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    Hello, I tried to solve a simple "problem" with an series rlc circuit at resonance, what i wanted to find was
    1) if voltage magnification will occur
    2)VL , VC , VR , I0
    3)The circuits power at resonance
    I attach two print screens of the circuit( given Vs, L,C,R) and my solution attempt.
    Is the way i try to solve it right ?
    http://prntscr.com/4jmlsg
    http://prntscr.com/4jmm8j
     
  2. MikeML

    AAC Fanatic!

    Oct 2, 2009
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    The circuit has such a low Q that the Voltage Magnification at V(a) is barely perceptible.

    Here is the complete solution. You can check to see if your work matches this:

    70.jpg
     
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  3. JoeJester

    AAC Fanatic!

    Apr 26, 2005
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    Here are two "cheat" sheets that talk about the characteristics of resonant circuits.
     
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  4. JoyAm

    Thread Starter Member

    Aug 21, 2014
    112
    4
    Thank you for your immediate answers Mike and Joe.
    What i really need to know is
    1) how will i know if a voltage magnification will occur ( what i can think of is to check the voltage on either capacitor or inductor (assuming I=Vs/R) and then check if its bigger than the one in the resistor, which will be the same with the source Vs , is that right ?)
    2) the power of the whole circuit will be Vs^2*R because the sum of the capacitor and inductor is zero ?
    Thanks in advance :)
     
  5. MikeML

    AAC Fanatic!

    Oct 2, 2009
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    I have never heard the term "voltage magnification" until your post. The concept is tied up to the Q of a resonant circuit, so read up on Q.
    I already showed you the power into the circuit (the expression V(1)*-I(V1) shown in the bottom plot pane). Since L and C are ideal, lossless components, then it follows that at resonance, the power in the resistor is the same as the input power.
     
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  6. JoyAm

    Thread Starter Member

    Aug 21, 2014
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    1)Maybe i am using the wrong term then. What i mean is that at resonance we have VL=-Vc and Vs=VR
    That makes the VL and VC able to much higher than Vs and when that happens we call it voltage magnification ( if there is another term that describes this phenomenon please let me know).
    2)So the power of the circuit at resonance is equal with the power in the resistor, right ?
     
  7. JoeJester

    AAC Fanatic!

    Apr 26, 2005
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    At best, Vc and Vl will be the Q x E line. Look at that cheat sheet for series resonant circuits at fr.
     
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  8. JoyAm

    Thread Starter Member

    Aug 21, 2014
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    So we come to the conclusion that in this circuit(with these values of Vs,R,L,C) even when it is at resonance, no voltage magnification occurs, am i right ?
    Also about your cheat sheet, i think that you use the value of Vs=10volt in your calculations, but when we are given the peak to peak voltage, dont we have to divide it by 2 to get the V0?
     
  9. JoeJester

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    Apr 26, 2005
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    When I used 10 volts pk to pk all other values were peak to peak.

    If I were going to use rms, I would have done more than divide by 2.

    If you were going to take the readings using an oscilloscope, they would be pk to pk.
     
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  10. MikeML

    AAC Fanatic!

    Oct 2, 2009
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    Here is a plot of the "magnification" that occurs in V(a) as a function of frequency with R1=1000. Note it increases only ~ 1%:

    205b.jpg

    Here is a plot with R1=10, a much higher Q:

    205c.jpg
     
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  11. JoyAm

    Thread Starter Member

    Aug 21, 2014
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    Well that what solved all my misunderstandings ( i was blind to it all the time although your were trying to make me see it )
    So to sum up, if Q>1 that means we will have a voltage magnification :)
    Thanks both of you once more
     
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