5. The following a series RLC circuit with R = 3 k ohm, L = 10H , and C = 200uF has a constant voltage source V = 5theta*VAC signal with a frequency of 60 Hz
Calculate the capacitive reactance and the inductive reactance in the circuit?
b. Determine the impedance?
c. Calculate the rms consumed in the circuit?
d. Calculate the voltage across the resistor, the inductor and the capacitor?
e. How much power is consumed in the circuit?
f. What is the resonant frequency of the circuit
a. Capacitive reactance XC = 1 / (2pi*f*C) = 1 / (2*3.14*60*200*10^-6) = 13.28 ohms
Inductive reactance XL = 2 * pi * f * L = 2 * 3.14 * 60 * 10 = 3770.79 ohms
b. Impedance Z = sqrt((R^2 + (XL - XC)^2)) = sqrt((3000^2 + (3770.79 - 13.28)^2)) = 4980.54 ohms
c. The rms current in the circuit is V / Z = 5 / 4980.54 = 0.0010025 A
The rms power consumed in the circuit is (I^2)R = (0.0010025^2) * 3000 = 3.008 W
d. Voltage across resistor VR = IR = 0.0010025 * 3000 = 3 V
Voltage across inductor VL = IXL = 0.0010025 * 3770.79 = 3.78 V
Voltage across capacitor VC = IXC = 0.0010025 * 13.28 = 0.04 V
e. Power consumed in the circuit = VR * I = 3 * 0.0010025 = 0.003 W
f. The resonant frequency of the circuit can be calculated using the formula f = 1 / (2 * pi * sqrt(L * C)) = 1 / (2 * 3.14 * sqrt(10 * 200 * 10^-6)) = 50 Hz