An RLC circuit is driven by an AC generator at f = 188 Hz frequency. (See figure

Question

An RLC circuit is driven by an AC generator at f = 188 Hz frequency. (See figure.) The elements of the circuit have the following values: R = 227 Ohm, L = 0.711 H, C = 6.58 mu F. What is the impedance of the circuit? (in Ohm) A: 2.45 times 10^2 B: 3.55 times 10^2 C: 5.15 times 10^2 D: 7.47 times 10^2 E: 1.08 times 10^3 F: 1.57 times 10^3 G: 2.28 times 10^3 H: 3.30 times 10^3 What is the resonant frequency of the circuit? (in Hz) A: 3.53 times 10^1 B: 3.99 times 10^1 C: 4.51 times 10^1 D: 5.10 times 10^-1 E: 5.76 times 10^1 F: 6.51 times 10^1 G: 7.36 times 10^1 H: 8.31 times 10^1

Explanation / Answer

xl = wl = 2pifl = 839.4 ohm

xc = 1/wc = 128.7 ohm

xl-xc = 710.7 ohm

z = sqrt(R^2+(xl-xc)^2) = 746.07 ohm

option d is correct

b) xl = xc

w = 1/sqrt(lc) = 462.32

f = w/2pi = 73.6 Hz

option G

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