RCL Physics?

Question

A series RCL circuit has a resonant frequency of 1530 Hz. When operating at a frequency other than 1530 Hz, the circuit has a capacitive reactance of 5.0 and an inductive reactance of 30.0 .

What is the value of the inductance (L)?

What is the value of C, the capacitance?

Answer 1

The impedence of series RLC circuit is
Z= sqrt[R^2 + (Lw - 1/Cw)^2]

at resonance w=wo, (wo=2*pi*fo & fo=1530 Hz (resonant freq.))

Z has to be the least (Z=R) or current the MAXIMUM >>>

Lwo = (1/Cwo) or wo^2 = 1/LC or

LC = 1 / 4*pi^2*fo^2 .....(1)

When this circuit operates on any other frequency (v), then

Inductive reactance= L.(2*pi*v) = 30 ---(2)
Capacitive reactance= 1 / (C*2*pi*v) = 5 ....(3)

multiply (2) and (3) L / C = 150 .......(4)

Multiply (1) and (4)

L^2 = [1 / 4*pi^2*fo^2] * 150 or L = sqrt(150)/2*pi*fo
L = 12.25/2*3.14*1350 =0.001444916 = 1444.916* 10-6
>>> L = 1444.916 micro henry
>>> C=L /150 = 9.6327 micro farad

--------------------
simplified:

LC = 1 / wo^2 (w0=resonant angular freq= 2*pi*fo) ....(1')

When this circuit operates on any other frequency (v=w/2pi), then

Inductive reactance= L.(w) = 30 ---(2')
Capacitive reactance= 1 / (C*w) = 5 ....(3')

multiply (2) and (3) L / C = 150 .......(4')

Multiply (1) and (4')

L^2 = [1 /wo^2] * 150 or
L = sqrt(150) / w0
L = 12.25 / 2*3.14*1350 = 1444.916* 10-6
>>> L = 1444.916 micro henry
>>> from (4') C=L /150 = 9.6327 micro farad

Answer 2

Inductive Reactance is X = wL and capacitive reactance is X = 1/wC

where w = 2(pi)f

In order to solve your problem we would need to know the frequency at which the measurements were taken.