RLC Circuits with a Generator?

Question

A series RLC circuit in a radio receiver is tuned by a variable capacitor, so that it can resonate at frequencies from 500 to 1600 kHz. If the inductance L=1 microH, find the range of capacitances necessary to cover this range of frequencies

Answer 1

The resonanct frequency of an RLC circuit is defined by:
Fr = 1/(sqrt(L*C)).
Set the left side equal to 500kHz and solve for C.
C = 4 micro Farads

Now set Fr = 1600kHz

C = 390.625 nano-Farads

Therefore 390.625nF

Answer 2

The first answer is nearly right except the formula refers to the frequency in radians per second. For frequency in Hz, it should be F = 1/(2*pi*sqrt(L*C)). Therefore C = 1/(L*(2*pi*F)^2). For 500 KHz, C = 101.3 nF and for 1600 KHz, 9.89 nF.

Answer 3

For resonance,
ωL = 1/ωC
C = 1/ω^2L
ω = 2πf
C = 1/(2πf)^2L
1/(2π1600000)^2(10^-6) ≤ C ≤ 1/(2π500000)^2(10^-6)
9.89 nf ≤ C ≤ 0.101 μf