Question

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

Short answer

The value of capacitance is $8.34\times {10}^{-18}$F.

Step-by-step solution

Given information

We have given that, an MRI machine oscillate at very high frequencies. It has inductance of 15 mH and frequency of signal is 450 MHz.

Step 1.

The formula to calculate the capacitance is :

$C=\frac{1}{L{\left(2\mathrm{\pi f}\right)}^2}$

Here, C = Capacitance

L = Inductance

f = Frequency

Step 2.

Substituting the values in the formula :

$C=\frac{1}{(15\times {10}^{-3}H){(2\mathrm{\pi }\times 450\times {10}^6\mathrm{Hz})}^2}$

$C=8.34\times {10}^{-18}F$.