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12 July, 01:00

The ratio of the inductive reactance to the

capacitivereactance is observed to be 5.36 in a series RCL circuit.

Theresonant frequency of the circuit is 225 Hz. What is the

frequency (nonresonant) of the generator that is connected to

thecircuit?

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Answers (1)
  1. 12 July, 02:03
    0
    The non resonance frequency of the generator is = 1201.79 Hz

    Explanation:

    At resonance,

    f₀ = 1/2π√LC ... Equation 1

    Where f₀ = resonance frequency, L = inductance, C = capacitance

    making LC the subject of the equation

    LC = 1/4πf₀² ... Equation 2

    Given: f₀ = 225 Hz, and π = 3.143

    Substituting these values into equation 2,

    LC = 1 / (4*3.143²*225²)

    LC = 1/2000385.9

    LC = 5*10⁻⁷

    If the ratio of capacitive reactance to inductive reactance = 5.36

    1/2πfC/2πfL = 5.36

    1/4π²f²LC = 5.36

    Where f = frequency of the non resonant

    making f the subject of the equation

    f = 5.36/2π√LC ... Equation 3

    Substituting the value of LC = 5*10⁻⁷ into equation 3

    f = 5.36/2*3.143√ (5*10⁻⁷)

    f = 5.36 / (6.286*0.00071)

    f = 5.36/0.00446

    f = 1201.79 Hz

    Thus the non resonant frequency of the generator is = 1201.79 Hz
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