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**

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