Question

An RLC series circuit has a 1.00 k? resistor, a 160 mH inductor, and a 25.0 nF capacitor. (a) Find the circuit's impedance (in ?) at 515 Hz. (b) Find the circuit's impedance (in ?) at 7.50 kHz. (c) If the voltage source has Vrms = 408 V, what is Irms (in mA) at each frequency? mA (at 515 Hz) mA (at 7.50 kHz) (d) What is the resonant frequency (in kHz) of the circuit? kHz (e) What is Irms (in mA) at resonance? mA

Answer 1

a)

impedance is z = sqrt(R^2+(XL-XC)^2)

R = 1000 ohm

XL = w*L = 2*3.142*515*0.160 = 517.8 ohm

XC = 1/(w*C) = 1/(2*3.142*515*25*10^-9) = 12359.94 ohm

z = sqrt(1000^2+(517.8-12359.94)^2) = 11884.3 ohm

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b) XL = 2*3.142*7.5*1000*0.160 = 7541 ohm

XC = 1/(2*3.142*7.5*1000*25*10^-9) = 848.72 ohm

Z = sqrt(1000^2+(7541-848.72)^2) = 6766.58 ohm

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C) at f =515 Hz

Irms = Vrms/Z = 408/11884.3 = 0.0343 A

at f = 7.5 kHz

Irms = Vrms/z = 408/6766.58 = 0.061 A

d) resonant frequency is f = 1/(2*pi*sqrt(L*C)) = 1/(2*3.142*sqrt(0.160*25*10^-9)) = 2516.13 Hz = 2.516 kHz

e) Irms = Vrms/R =408/1000 = 0.408 A = 408 mA