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19 April, 16:54

An fm radio station broadcasts at a frequency of 91 mhz. part a what inductance should be paired with a 9.0 pf capacitor to build a receiver circuit for this station?

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  1. 19 April, 18:19
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    It's not clear exactly how you intend to use an ' L ' and a ' C ' in a

    receiver circuit.

    Perhaps you just want a simple resonant 'tank', so that the voltage

    across it peaks at 91 MHz. Then you just want to know what parallel

    L-C is resonant at 91 MHz.

    Without resistance to complicate things, the resonant frequency

    of a parallel L-C is

    f = 1 / [ 2π √ (LC) ].

    Before we get tangled up in this thing,

    let's just solve it for ' L ':

    Multiply each side by √ (LC), then divide each side by f,

    and then it says

    √ (LC) = 1 / (2π f)

    Divide each side by √C:

    √L = 1 / 2πf√C

    then square each side:

    L = 1 / (4 · π² · f² · C)

    and now we can easily go ahead and find ' L '.

    L = 1 / (4 · π² · 91² · 10¹² · 9 · 10⁻¹²)

    When I stuff that through my calculator, I get

    L = 0.34 microhenry
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