Question

An fm radio station broadcasts at a frequency of 91 mhz . part a what inductance should be paired with a 9.0 pf capacitor to build a receiver circuit for this station?

Answer 1

It's not clear exactly how you intend to use an ' L ' and a ' C ' in a
receiver circuit.

Perhaps you just want a simple resonant 'tank', so that the voltage
across it peaks at 91 MHz. Then you just want to know what parallel
L-C is resonant at 91 MHz.

Without resistance to complicate things, the resonant frequency
of a parallel L-C is

f = 1 / [ 2π √(LC) ].

Before we get tangled up in this thing,
let's just solve it for ' L ' :
Multiply each side by √(LC), then divide each side by f ,
and then it says

√(LC) = 1 / (2π f)

Divide each side by √C :

√L = 1 / 2πf√C

then square each side:

L = 1 / (4 · π² · f² · C)

and now we can easily go ahead and find ' L '.

L = 1 / (4 · π² · 91² · 10¹² · 9 · 10⁻¹²)

When I stuff that through my calculator, I get

L = 0.34 microhenry