Question

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5. + -11 points SerPSE 10 32.7.P.026. A series RLC circuit has components with the following values: L = 18.0 mH, C = 80.0 nF, R = 30.0 2, and AVmax = 100 V, with Av = AV may sin wt. (a) Find the resonant frequency of the circuit. kHz (b) Find the amplitude of the current at the resonant frequency. (c) Find the Q of the circuit. (d) Find the amplitude of the voltage across the inductor at resonance.

Answer 1

PART A:

For a series RLC circuit, the resonance frequency is given by

fr= LC

Putting the values in SI units

fr = = 4194 Hz = 4.194 kHz 27 21 (18 x 10-3) (80 x 10-9)

So, the answer is 4.194 kHz.

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PART B:

The impedence of the circuit at the resonant frequency is

7=R=30

So, the amplitude of the current at the resonant frequency is

I= = = 500 = 3.33 A

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PART C:

The quality factor of the circuit at the resonant frequency is given by

본 이

-1.18 x 10-3 30 V 80 X 10-9 = 15.81

So, the answer is 15.81.

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PART D:

We have

XL = 2nf L = 27 x 4194 x 18 x 10-3 = 474.332

So, the amplitude of the voltage across the inductor at resonance is

Vi = XI = 474.33 X 3.33 = 1579.5 V = 1.58 kV

So the answer is 1.58 kV.