LC oscillators have. been used to circuits. connected to loud speakers to create some of the sounds of electronic musc. What indductance mus

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LC oscillators have. been used to circuits. connected to loud speakers to create some of the sounds of electronic musc. What indductance must be usedd with a 6.7 uF capacito r to prodice a frequncy of 10

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Gerda 1 year 2021-09-03T04:23:08+00:00 1 Answers 5 views 0

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    2021-09-03T04:24:09+00:00

    Answer:

    [tex]3.8\times 10^{-8}\ H[/tex]

    Explanation:

    Given the [tex]6.7\mu F[/tex] capacitor is used in an LC circuit to produce [tex]10\ kHz[/tex] frequency.

    We need to find the value of inductance required.

    As we know the relation between angular frequency in [tex]rad/sec[/tex] and frequency in [tex]Hz[/tex] is.

    [tex]\omega =2\times \pi\times f[/tex]

    Where [tex]\omega[/tex] is angular frequency and [tex]f[/tex] is frequency.

    [tex]\omega=2\times \pi\times 10\times 1000=20000\pi\ rad/sec\\\omega=62832\ rad/sec[/tex]

    Also, the relation between the angular frequency, capacitance and inductance is given by.

    [tex]\omega^2=\frac{1}{LC}\\\\L=\frac{1}{\omega^2C} \\\\L=\frac{1}{62832^2\times6.7\times 10^{-6} } \\\\L=\frac{1}{26451}.\\ \\L=3.8\times 10^{-8}\ H[/tex]

    So, [tex]3.8\times 10^{-8}\ H[/tex] inductance will be required to produce [tex]10\ kHz[/tex].

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