An FM radio station broadcasts at a frequency of 100 MHz. What inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station?
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Step 1
To pair emitter and receiver of FM signal, the frequency of both devices must be the same. So we have to compute the value the value of inductance L in order to have the circuit frequency oscillating at 100 MHz.
$f=\frac{1}{2\cdot \pi \sqrt{L\cdot C}}$
Lets

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Step 1
Resonant frequency, $f=100MHz$
capacitance, $C=10pF$
The formula of the resonant frequency is
$f=\frac{1}{2\pi \sqrt{LC}}$
Step 2
Resonant frequency, $f=100MHz$
capacitance, $C=10pF$
Let the inductance is L.
Substitute the values in the formula
$100×{10}^{6}=\frac{1}{2\pi \sqrt{L×10×{10}^{-12}}}$
$4{\pi }^{2}×{10}^{16}=\frac{1}{L×{10}^{-11}}$
$L=2.54×{10}^{-7}H$