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24 June, 04:34

A parallel RLC resonant circuit has a resistance of 200 Ω. If it is known that the bandwidth is 80 rad/s and the lower half-power frequency is 800 rad/s, find the values of the parameters L and C.

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  1. 24 June, 06:36
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    L = 3.6mH

    C = 9.9 microfarad

    Explanation:

    Resonant frequency fr

    fr = fl + 1/2 BW

    fr = 800 + 1/2*80

    =800+40

    =840 rad/s

    Bandwidth (BW)

    BW = fr/Q

    Q = quality factor

    Q = fr / BW

    Q = 840/80

    Q = 10.5

    Quality factor = R/Xl

    Xl = inductive reactance

    Xl = R/Q

    Xl = 200/10.5

    Xl = 19.05 ohms

    Xl = 2πfL

    L = Inductance

    L = Xl / 2πf

    L = 19.05/5278.56

    L = 3.6mH

    Capacitor C

    1 = fr^2 * 4π^2LC

    C = 1/fr^24π^2L

    C = 1/100307.5

    C = 9.9microfarad
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