Problem 12: An RLC series circuit has a 2.4 ohm resistor, a 95 mu H inductor, an
ID: 1605297 • Letter: P
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