Explore BrainMass

Explore BrainMass

    Resistors, Inductors, and Capacitors

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    1- Assume a passive network N composed of resistors, inductors, and capacitors

    A- How can you modify N such that each and every natural frequency is shifted one unit to left? (i.e. its real part is reduced by 1)
    B- How can you modify N such that each and every natural frequency is shifted one unit to right? (i.e. its real part is increased by 1)

    © BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf
    https://brainmass.com/physics/resistors/resistors-inductors-capacitors-14849

    SOLUTION This solution is FREE courtesy of BrainMass!

    Please find the solution in the attachment.
    In this problem, you are basically asked to find out how can you affect N so that resonance can be altered.

    Since for a RLC circuit, the resonant frequency is given by

    Wo = 1/ sqrt (LC)

    Since in your case, it's a network of N, equation becomes

    Wo = 1/ N sqrt (LC) ---------------------- (1)

    Case 1)

    To reduce the natural frequency by changing N, (keeping RLC unchanged)

    W1 = 1/ N' sqrt (LC) -------------------------- (2)

    Dividing (1) by (2), we have

    So, N' = N ( Wo/ W1)

    But W1 = W0 - 1

    Hence N' = N ( Wo / Wo - 1)

    Increase the Number of RLCs by N'

    Case (2)

    Here W1 = W0 + 1

    Hence N' = N ( Wo / Wo + 1)

    Reduce the number of RLCs by N'

    Aside : for RLC,

    Output impedance Z = sqrt ( R^2 + (Xl - Xc) ^2)

    At resonance Xl = Xc so that Z = R; which leads us to the resonance frequency

    Wo = 1/ sqrt (LC) ; ( Xl = j WL ; Xc = 1/j W c )

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

    © BrainMass Inc. brainmass.com December 24, 2021, 4:54 pm ad1c9bdddf>
    https://brainmass.com/physics/resistors/resistors-inductors-capacitors-14849

    Attachments

    ADVERTISEMENT