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    RLC Circuit: Resonance

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    An RLC circuit has a capacitance of 0.43 microF.

    (a) What inductance will produce a resonance frequency of 95 mHz?

    (b) It is desired that the impedance at resonance be 1/2 the impedance at 11 kHz. What value of R should be used to obtain this result?"

    © BrainMass Inc. brainmass.com October 6, 2022, 1:55 pm ad1c9bdddf
    https://brainmass.com/physics/resonance/rlc-circuit-resonance-38395

    SOLUTION This solution is FREE courtesy of BrainMass!

    Z =impedance = square root of {R + (X L ^2 -XC^2)}

    XL= reactance of inductor = 2 pi f L
    XC= reactance of capacitor = 1/ (2 pi f C)

    (a) What inductance will produce a resonance frequency of 95 mHz?
    At resoance Z = R and XL=XC

    2 pi f L = 1/ (2 pi f C)

    L = 1/ {C (2pi f ) ^2}
    C= 0.00000043 F
    f= 95000000 Hz
    Therefore L= 6.5E-12 H

    (b) It is desired that the impedance at resonance be 1/2 the impedance at 11 kHz. What value of R should be used to obtain this result?"

    Impedance at resonance =R

    impedance at 11 kHz:

    Z =impedance = square root of {R^2+ (X L ^2 -XC^2)}

    XL= reactance of inductor = 2 pi f L
    XC= reactance of capacitor = 1/ (2 pi f C)

    L= 6.5E-12 H
    C= 0.00000043 F
    f= 11000 Hz

    XL= reactance of inductor = 2 pi f L= 0.00000045
    XC= reactance of capacitor = 1/ (2 pi f C)= 33.65

    At this frequency the reactance of the inductor is negligible

    therefore Z= square root of {R^2+ (XC^2)}

    For the impedance at resonance to be 1/2 the impedance at 11 kHz

    impedance at resonance = R = 1/2square root of {R^2+ (XC^2)}

    Squaring both sides
    R^2= 1/4 (R^2+ XC^2)

    or 3/4 R^2=1/4 (XC^2)

    Bur XC= 33.65
    Therefore R= 19.43 ohm

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 6, 2022, 1:55 pm ad1c9bdddf>
    https://brainmass.com/physics/resonance/rlc-circuit-resonance-38395

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