Problem 12: An RLC series circuit has a 2.4 ohm resistor, a 95 mu H inductor, an

Question

Problem 12: An RLC series circuit has a 2.4 ohm resistor, a 95 mu H inductor, and a 87.5 um F capacitor. Part (a) Find the circuit's impedance, in ohms, at 110 Hz. Z_1 = _______ Part (b) Find the circuit's impedance, in ohms, at 55 kHz. Part (c) If the voltage source supplies an rms voltage of 554 V, what is the circuit's rms current, in amperes, at a frequency of 110 Part (d) If the voltage source supplies an rms voltage of 554 V, what is the circuit's rms current, in amperes, at a frequency of 55 Part (e) What is the resonant frequency, in kilohertz, of the circuit? Part (f) What is the rms current, I_rms in amperes, at resonance?

Explanation / Answer

a)

Impedence is z = sqrt(R^2+(XL-Xc)^2)

Xc = 1/(w*C) =1/(2*pi*f*C) = 1/(2*3.142*110*87.5*10^-6) = 16.54 ohm

XL = 2*pi*f*L = 2*3.142*110*95*10^-6 = 0.06566 ohm

then Z = sqrt(2.4^2+(0.06566-16.54)^2) = 16.64 ohm

b) for f = 5.5 kHz

Xc = 1/(w*C) =1/(2*pi*f*C) = 1/(2*3.142*5.5*1000*87.5*10^-6) = 0.33 ohm

XL = 2*pi*f*L = 2*3.142*5.5*1000*95*10^-6 = 3.28 ohm

then Z = sqrt(2.4^2+(3.28-0.33)^2) = 3.8 ohm

C) Irms = Vrms/Z =5.54/16.64 = 0.332 A

D) Irms = Vrms/Z = 5.54/3.8 = 1.46 A

e) at resonance XL = Xc

then f = 1/(2*pi*sqrt(L*C)) = 1/(2*3.142*sqrt(95*10^-6*87.5*10^-6)) = 1745.42 Hz = 1.75 kHz

f) Irms = Vrms/R = 5.54/2.4 = 2.3 A

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