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    The graph shows the variation of current I with the frequency ω in an LCR circuit. What is the bandwidth?
    Question

    The graph shows the variation of current I with the frequency ω in an LCR circuit. What is the bandwidth?

    A.

    4 rad s⁻¹

    B.

    0.6 rad s⁻¹

    C.

    1.2 rad s⁻¹

    D.

    0.4 rad s⁻¹​

    Correct option is C

    Correct answer is C
    Explanation
    We know that the bandwidth is given by:
    Bandwidth = (ω2 - ω1)
    Here, ω1 and ω2 are the two angular frequencies at which the current amplitude of the LCR circuit becomes Imax / √2. At this point, the current is 0.707 times its maximum value, and the current reaches its peak at the resonant frequency.
    The RMS value of current can be expressed as:
    I = E0 / √2 = 1 / √2 = 0.707 A
    From the graph, the frequencies corresponding to 0.707 A current are:
    ω1 = 0.8 rad/s    and    ω2 = 1.2 rad/s
    Therefore, the bandwidth can be calculated as:
    Bandwidth = ω2 - ω1 => 1.2 - 0.8 = 0.4 rad/s
    Hence, the bandwidth of the given LCR circuit is 0.4 rad/s.

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