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 the diagram is series circuit
a. 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 / (2πfC) = 1 / (2π * 60 * 200e-6) ≈ 1.33 k ohm
Inductive reactance XL = 2πfL = 2π * 60 * 10 ≈ 3.77 k ohm
b.
Impedance Z = √(R^2 + (XL - XC)^2) = √(3^2 + (3.77 - 1.33)^2) ≈ 3.63 k ohm
c.
The rms current in the circuit can be calculated using Ohm's Law:
I = V / Z = 5 / 3.63 ≈ 1.38 A
The rms power consumed in the circuit is:
P = Vrms * Irms = 5 * 1.38 ≈ 6.92 W
d.
Voltage across the resistor VR = I * R = 1.38 * 3 ≈ 4.15 V
Voltage across the inductor VL = I * XL = 1.38 * 3.77 ≈ 5.20 V
Voltage across the capacitor VC = I * XC = 1.38 * 1.33 ≈ 1.84 V
e.
The total power consumed in the circuit is the same as the power calculated in part c, which is approximately 6.92 W.
f.
The resonant frequency of the circuit can be calculated using the formula:
f0 = 1 / (2π√(LC)) = 1 / (2π√(10 * 200e-6)) ≈ 795.8 Hz