Question

An RLC series circuit has a 3.00 k? resistor, a 55mH inductor, and a 30nF capacitor.

a) Find the circuit

Answer 1

a) at f = 460 hz

inductive reactance, XL = 2*pi*f*L =2*pi*460*0.055 = 159 ohm

capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*460*30*10^-9) = 11533 ohm

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

= sqrt(3000^2 + (159 - 11533)^2)

= 11763 ohms ---------->>>>>>>>>>>>>>>>>>>>Answer
b)
at f = 13.8 k hz = 13800

inductive reactance, XL = 2*pi*f*L =2*pi*13800*0.055 = 4769 ohm

capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*13800*30*10^-9) = 384.4 ohm

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

= sqrt(3000^2 + (4769 - 384.4)^2)

= 5313 ohms ---------->>>>>>>>>>>>>>>>>>>>Answer

3) Irms = Vrms/z

= 120/5313

= 0.0226 A or 22.6 mA ---------->>>>>>>>>>>>>>>>>>>>Answer

4) fo = 1/(2*pi*sqrt(L*C)

= 1/(2*pi*sqrt(0.055*30*10^-9))

= 3918 Hz ---------->>>>>>>>>>>>>>>>>>>>Answer

5) at resosnance, Z = R = 3 k ohm or 3000 ohms ---------->>>>>>>>>>>>>>>>>>>>Answer