Question

11. A circuit consists of a variable frequency A.C. Voltage source that supplies 120V peak, and a 10Ohms resistor, a 150?F capacitor, and a 150mH inductor, all in series. **PLEASE INCLUDE FORMULA FOR EACH PART*

A) calculate the RMS voltage

B) calculate the resonant frequency

C) calculate the inductive reactance at the resonant frequency

D) calculate the quality factor for the resonant circuit

Answer 1

Since its a series RLC circuit: (Since the unit of capaitance is not clear: i am assuming it to be uF as in most of the cases)

1. RMS volatge = peak voltage x 0.7071 : 120 x 0.7071 = 84.852 v

2. Resonant Frequency (f) = 1/ (2 x pi x (L x C)^1/2?): 1/ (2 x 3.14 x (0.15 x 150 x 10^-6)^1/2?) = 33.67 Hz

3. Inductive reactance at resonance frequency (X_L?) = 2 x pi x f x L = 2 x 3.14 x 33.67 x 0.15 = 31.72 ohm

4. Quality factor = 1/R x (L/C)^1/2 = X_L?/R = 31.72/10 = 3.172