An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15mH coil. To wha

Question

An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15mH coil. To what value should the capacitance be set to detect a 450 MHz signal?

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Khánh Gia 6 months 2021-08-15T15:20:21+00:00 1 Answers 34 views 0

Answers ( )

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    2021-08-15T15:21:32+00:00

    Answer:

    The capacitance is  C =  3.2 9  *10^{-16} \  F

    Explanation:

    From the question we are told that

       The  induction of the LC circuit is  L  = 15 mH  =  15 *10^{-3} \ H

        The  frequency is   w = 450 \ MHz =  450 *10^{6} \ Hz

    The natural frequency is mathematically represented as

              w =  \frac{1}{\sqrt{LC} }

    Where C is the capacitance So  

    =>      C =  \frac{1}{L * w^2}

    substituting values

             C =  \frac{1}{15 *10^{-3} * [450 *10^{6}]^2}

             C =  3.2 9  *10^{-16} \  F

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