Question

Answer all after part A

An RLC series circuit has a 2.25 Ohm resistor, a 105 Mu H inductor, and a 72.5 Mu F capacitor Find the circuit's impedance, in ohms, at 150 Hz. Find the circuit's impedance, in ohms, at 6.5 kHz. If the voltage source supplies an rms voltage of 5.66 V, what is the circuit's rms current, in amperes, at a frequency of 150 If the voltage source supplies an rms voltage of 5.66 V, what is the circuit's rms current, in amperes, at a frequency of 6.5 What is the resonant frequency, in kilohertz, of the circuit? What is the rms current, I_rms, in amperes, at resonance?

Answer 1

given

R = 2.25 ohms

L = 105 micro H

C = 72.5 micro F

a) f = 150 hz

capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*150*72.5*10^-6) = 14.63 ohms

Inductive reactance, XL = 2*pi*f*L = 2*pi*150*105*10^-6 = 0.099 ohms

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

= sqrt(2.25^2 + (14.63 - 0.099)^2)

= 14.7 ohms

b) f = 6.5 k hz = 6500 hz

capacitive reactance, XC = 1/(2*pi*f*C) = 1/(2*pi*6500*72.5*10^-6) = 0.338 ohms

Inductive reactance, XL = 2*pi*f*L = 2*pi*6500*105*10^-6 = 4.29 ohms

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

= sqrt(2.25^2 + (0.338 - 4.29)^2)

= 4.55 ohms

c) Irms = Vrms/z = 5.66/14.7 = 0.385 A

d) Irms = Vrms/z = 5.66/4.55 = 1.24 A

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

= 1/(2*pi*sqrt(105*10^-6*72.5*10^-6))

= 1824 hz

f) Irms = Vrms/z

= Vrms/R

= 5.66/2.25

= 2.516 A