An RLC series circuit has a 1.00 k resistor, a 165 mH inductor, and a 25.0 nF ca

Question

An RLC series circuit has a 1.00 k resistor, a 165 mH inductor, and a 25.0 nF capacitor. (a) Find the circuit's impedance at 495 Hz. Incorrect: Your answer is incorrect. . (b) Find the circuit's impedance at 7.50 kHz. Incorrect: Your answer is incorrect. . (c) If the voltage source has Vrms = 408 V, what is Irms at each frequency? Incorrect: Your answer is incorrect. . mA (at 495 Hz) Correct: Your answer is correct. . mA (at 7.50 kHz) (d) What is the resonant frequency of the circuit? Correct: Your answer is correct. . kHz (e) What is Irms at resonance? Correct: Your answer is correct. . mA

Explanation / Answer

R = 1000 ohm

L = 0.165 H

C = 25*10^-9 F

f1 = 495 Hz

f2 = 7500 Hz

Vrms = 408 V

a) XL = 2pi*f1*L = 2pi*495*0.165 = 513.2 ohm

Xc = 1/(2pi*f*C) = 12861 ohm

X = Xc - XL = 12347.8 ohm

Impedence = Z1 = sqrt[R^2 + X^2] = 12388.23 ohm

b) XL = 2pi*f1*L = 2pi*7500*0.165 = 7775.44 ohm

Xc = 1/(2pi*f*C) = 848.83 ohm

X = Xc - XL = 6926.61 ohm

Impedence = Z2 = sqrt[R^2 + X^2] = 6998.42 ohm

c) I1 = V/Z1 = 408/12388.23 = 32.93 mA

I2 = V/Z2 = 408/6998.42 = 58.3 mA

d) Resonant frequency = 1/2pi*sqrt(LC) = 2478.04 Hz

e) XL = 2pi*f1*L = 2pi*2478.04*0.165 = 2569.05 ohm

Xc = 1/(2pi*f*C) = 2569.05 ohm

X = Xc - XL = 0 ohm

Impedence = Z = sqrt[R^2 + X^2] = 1000 ohm

Current = I = 408/1000 = 408 mA

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