Question

A continuous AC voltage with peak voltage of 6 V and frequency f=732398 Hz is connected with a resistor (R-220 Ω), a capacitor with C-0.1 μΕ and an an inductor with L=680 nH. What is the capacitive reactance? What is the inductive reactance? What is the impedance when all three components are connected in SERIES? What is the current when all three components are connected in SERIES? What is the impedance of the circuit when all three components are connected in PARALLEL with the AC Voltage source? cted in PARALLEL with the AC Voltage source? What is the current when all three components are conne Hz What is the resonant frequency for BOTH circuits? What is the impedance in the circuit at the resonant frequency? What is the current in the circuit at the resonant frequency?

Answer 1

F = 732398 H_2 R = 220. C = 0.4 mu F. L = 630 n H. (a) x_c = 1/wc = 1/2 pi fc = 1/2 pi times 732398 times 0.1 times 10^-6 = 2.174 Ohm. x_c = 2.174 Ohm (b) x_L = 2 pi f L = 2 pi times 732398 times 680 times 10^-2 = > x_L = 3.128 Ohm (c) z = squareroot R^2 + (x_L - x_L)^2 = squareroot 220^2 + (3.128 - 2.174)^2 = 200.0021 Ohm z = 2_20.0021 Ohm (d) I = v/z = 6/2_20.0021 = 27.27 times 10^-3 A. I = 0.0273 A (e) z = 1/squareroot (1/R)^2 + (1/x_L - 1/x_L)^2 = 1/[(1/220)^2 + (-1/3.128 + 1/2.174)^L]^1/2 z = 7.124 Ohm (f) I = 6.0/7.124 = > I = 0.842 A (g) w = 1/squareroot L^c = > f = 1/2 pi. squareroot 1/L^c = 1/6.28 times 1/squareroot 680 times 0.1 times 10^-6 times 10^-5 f = 610640.9 H_2