Chapter 19B: AC Circuits » Bonus Question: RLC circuit An RLC circuit is driven

Question

Chapter 19B: AC Circuits » Bonus Question: RLC circuit An RLC circuit is driven by an AC generator at f = 181 Hz frequency.

The elements of the circuit have the following values: R = 220 , L = 0.508 H, C = 5.99 F. What is the impedance of the circuit? (in Ohm)

A: 5.21×101 B: 7.55×101 C: 1.09×102 D: 1.59×102 E: 2.30×102 F: 3.34×102 G: 4.84×102 H: 7.02×102

What is the resonant frequency of the circuit? (in Hz)

A: 6.32×101 B: 7.15×101 C: 8.07×101 D: 9.12×101 E: 1.03×102 F: 1.17×102 G: 1.32×102 H: 1.49×102

Explanation / Answer

1) The circuit impedance, Z = sqrt[R^2 + (XL-Xc)^2]
With f = 181 Hz
XL= 2 x pi x f x L = 2*pi*181*0.508 = 577.73 Ohm
Xc=1/(2 x pi x f x C) =146.8 Ohm
Z = 483.84 Ohm (option G is correct)

2) Resonant frequency, fr = 1/(2 x pi x sqrt[LC])
fr = 91.24 Hz (option D is correct)

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