Posted by Lauren on Thursday, August 2, 2012 at 8:37pm.
A series RCL circuit has a resonant frequency of 1500 Hz. When operating at a frequency other than 1500 Hz, the circuit has a capacitive reactance of 5.0 Ù and an inductive reactance of 30.0 Ù. What are the values of (a) L and (b) C?
I know I should be using these 2 equations:
Since each have 2*pi*f in them, with rearranging and substituting, you get:
However, with this it leaves the 2 unknowns, and I'm not sure what other equations I could use?
Physics - Elena, Friday, August 3, 2012 at 2:41am
f=1500 Hz, X(C)=5Ω, X(L)=30 Ω
Multiply (1) by (2):
X(C) •X(L)= ωL/ ωC =L/C.
C=L/X(C) •X(L) …..(3)
Resonant frequency is
Equate (3) and (4)
L/X(C) •X(L) =1/4•π²•f²•L,
C= L/X(C) •X(L)=
= 8.67 μF
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