91Ó°ÊÓ

We have given that, an FM radio station broadcasts at a frequency of 100 MHz, and receiver circuit for this station has 10 pF capacitor.

The formula to calculate the inductance is :

$L=\frac{1}{{\mathrm{Ó\neg }}^{2}C}$

Here, $L$= Inductance

$\mathrm{Ó\neg }$= Resonant frequency

$C$= Capacitance

We have to get value of resonant frequency first.

Formula of resonant frequency is :

localid="1650299962559" $\mathrm{Ó\neg }=\left(2\mathrm{Ï€}\mathrm{f}\right)$

Here, $\mathrm{Ó\neg }=$Resonant frequency

f = Frequency at which station broadcast

Substituting the values in the formula of resonant frequency :

localid="1651031527615" $\mathrm{Ó\neg }=2\mathrm{Ï€}(100×{10}^{6}Hz)$

localid="1650300275603" $\mathrm{Ó\neg }=6.28×{10}^{8}Hz$

Now we will substitute all the values in the formula of inductance.

Substituting the values in the inductance formula :

$L=\frac{1}{{\mathrm{Ó\neg }}^{2}C}$

localid="1651032743574" $L=\frac{1}{{(6.28×{10}^{8}Hz)}^2(10×{10}^{-12}F)}$

$L=2.5×{10}^{-7}H=0.25\mathrm{μ}H$

$0.25\mathrm{μ}H$inductance should be paired with a 10 pF capacitor to build a receiver circuit for this station.