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-power frequency is 800 rad/s, find the values of the parameters L and C.

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Physics

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24 June, 04:34

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-power frequency is 800 rad/s, find the values of the parameters L and C.

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Frankfurter · Answer 1

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