RLC question (complicated)

  1. I find this question very hard and i could not work out the answers, i have looked on the internet for forumals but they don't seem to work ??
    Anyone got any methods to work through the question ???

    I found a website that is about RLC series circuits but looking into it, it really confuses me with all the equations:

    http://www.tpub.com/neets/book2/4l.htm

    An RLC series circuit has a resonant frequency of 1.2kHz and Q factor at resonance of 50. If the impedance of the circuit is 75 ohms calculate the values of:

    a. the inductance vaule
    b. the capacitance value
    c. the bandwidth
    d. the lower and upper half-power frequencies
    e. the vaules of the circuit impedance at the half power frequencies.

    Thanks
     
    Last edited: Jun 16, 2005
  2. jcsd
  3. SGT

    SGT 0

    The resonant frequency of a LC circuit is:
    [tex]\omega_0 = \frac{1}{\sqrt{LC}}[/tex]
    And the quality factor is:
    [tex]Q = \omega_0 RC[/tex]
    Since it is given a real value for the impedance, we must assume that this value is calculated at the resonant frequency.
    Z = R.
    So, you know ω0, Q and R. You have two equations and two unknowns: L and C.
     
  4. done it !!!

    ok here is the equation i used

    Q = XL/R = XC/R

    Q x R = XL 50 x 75 = 3750 ohms

    Q x R = XC 50 x 75 = 3750 ohms

    then just use XL = 2pie FL
    and
    XC = 1 / 2pie FC

    transpose that !!!!

    L = 2pie F / XL

    C = 1 / 2pie F XC

    But one more question, what equation can i use to get the lower and upper half power frequencies ???
     
  5. SGT

    SGT 0

    You have:
    [tex]Q = \frac {\omega_0}{\omega_2 - \omega_1}[/tex]
    Where [tex]\omega_0[/tex] is the resonant frequency and [tex]\omega_1[/tex], [tex]\omega_2[/tex] the half power frequencies.
     
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