physics problem need help?

Question

A series RLC circuit has a resonance frequency of 2000/ Hz. When it is operating at a frequency of w>w0, XL = 13.0 and XC = 9.0 . Calculate the values of L and C for the circuit.

C = µF
L = mH

Answer 1

From the formula for resonant frequency we know that

f0 = 1/(2*PI*SQRT(LC))

SQRT(LC) = 1/(2*PI*f0)

LC = (1/(2*PI*f0))^2 = 6.3x10^-9 (eq 1)

Using the formulas for reactance,

XL = 2*PI*f*L

L = XL/(2*PI*f) (eq 2)

XC = 1/(2*PI*f*C)

C = 1/(2*PI*f*XC) (eq3)

Write eq 1 to give you L and subsitiute into eq 2.

Use eq 2 and eq 3 to eliminate f, the frequency, and obtain C, then work backwards to obtain L.