A parallel RLC resonant circuit has a resistance of 200 Ω. If it is known that the bandwidth is 80 rad/s and the lower half-powe r frequency is 800 rad/s, find the values of the parameters L and C.
1 answer:
Answer:
L= 3.6mH
C =9.9 microfarad
Explanation:
Resonant frequency fr
fr = fl + 1/2 BW
fr = 800+ 1/2×80
=800+40
=840 rad/s
Bandwidth (BW)
BW = fr/Q
Q = quality factor
Q= fr/ BW
Q = 840/80
Q= 10.5
Quality factor = R/Xl
Xl = inductive reactance
Xl = R/Q
Xl = 200/10.5
Xl = 19.05 ohms
Xl =2πfL
L= Inductance
L = Xl /2πf
L =19.05/5278.56
L= 3.6mH
Capacitor C
1= fr^2 × 4π^2LC
C = 1/fr^24π^2L
C = 1/100307.5
C= 9.9microfarad
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