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?

Answer 1

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

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

         $C = 3.2 9 *10^{-16} \ F$