Maximum and minimum values of a variable capacitor

[rlc]

Homework Statement

A parallel circuit like that in the figure forms the tuning circuit for an AM radio. If the inductor has a value of 8.6×10-6 H, what must be the maximum and minimum values of the variable capacitor if the radio receives frequencies from 590k Hz to 1670k Hz?
a) Maximum C?
b) Minimum C?

Homework Equations

w=2*pie*f
f=1/(2*pie*sqrt(LC))

sqrt(LC) = 1 / (2 pi f)
LC = 1 / (2 pi f)^2
C = 1 / [ (2 pi f}^2 L)

The Attempt at a Solution

Is the inductor value 8.6E-6 H the variable f in the equation? Are those equations even the ones I use?
590k Hz= 5.9E5 Hz
How do I begin this problem? I'm just really confused

 

[gneill]

Is the inductor value 8.6E-6 H the variable f in the equation? Are those equations even the ones I use?

By convention the variable name used for inductance is L. f is frequency. C is capacitance.

 

[rlc]

C = 1 / [(L)(4pi^2)(f^2)]
Cmax= 1 / [(8.6E-6)(4pi^2)(590E3)^2]
Cmax=8.461E-9 F

Cmin=1 / [(8.6E-6)(4pi^2)(1670E3)^2]
Cmin=1.056E-9 F

*I kept getting this wrong because the equation in the Relevant Equations part had a 2 instead of a 4*