Question

J# 10: 29:2018: Monday Show all steps for full credit. 1. What is the resonance frequency of an LC circuit consisting of a capacitor of s microfarads and a 0.06 Henries. inductor? Lc 2. In a RLC series circuit, the rms voltage of the ac power supply is 120 Volts. The frequency is 45 Hertz. It has a resistance of 100 ohms and a capacitance of 60 micro farads and inductance of 65milli henries. Calculate a) the inductive reactance b) the capacitive reactance c) reactance d) impedance e) rms current. f) current amplitude

Answer 1

1.

Given

LC circuit with C = 55*10^-6 F, L = 0.06 H

the resonance frequency when W_L = W_C

LC circuit resonance frequency is f_r = (1/(2pisqrt(L*C))

f_r = 1/(2pi(sqrT(0.06*55*10^-6))) Hz

f_r = 87.61 Hz  

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2.

LCR circuit with , e = 120 V, f = 45 Hz

R = 100 ohm

C = 60*10^-6 F,

L = 65*10^-3 H

a) inductive reactance is X_L = W*L = 2pi*f*L = 2pi*45*65*10^-3 ohm = 18.38 ohm

b) capacitive reactance is X_C = 1/(W*C) = 1/(2pi*f*C) = 1/(2pi*45*60*10^-6) ohm = 58.95 ohm

c) reactance is X_c -X_L = 58.95-18.38 ohm = 40.57 ohm

d) impedance is Z = sqrt(R^2+(X_C-X_L)^2)

Z = sqrt(100^2+ 40.57^2) ohm = 107.92 ohm

e) rms current Irms = I_m/(sqrt(2))

I_m = (e/Z) = 120/107.92 A = 1.11 A

Irms = 1.11/(sqrt(2) A = 0.785 A

f) current amplitude is I_m = 1.11 A