Question

2. For the circuit shown in (c), above, let R-200, L--10mH, and C-001μF. a. (2pts) Find the resonant frequency, ao . b. (4pts) Find the current in the network for a sinusoidal voltage source, Vin 0.5 VRMS at an angular frequency of ω ω0. C. (3pts) Find the voltage dropped across the capacitor for the parameters of part (b) d. (2pts) What is the quality, Q, of the network?

Answer 1

Given R = 20 ohm L = 10 mH c = 0.01 mu F (a) Resonant frequency w_0 = 1/squareroot LC 2pi f_r = 1/squareroot LC f_r = 1/2pi squareroot LC = 1/2 times 3.14 times squareroot 10 times 10^-3 times 0.01 times 10^-6 f_r = 1/6.28 times 10^-5 Resonant frequency f_r = 15.923 kHz (b) x_L = w_0 L = 2pi fL = 2 times 3.14 times 15.923 times 10^3 times 10 times 10^-3 x_L = 999.964 H x_c = 1/wc = 1/w_0 C = 1/2pi fc = 1/2 times 3.14 times 15.923 times 10^3 times 0.01 times 10^-6 x_c = 1000.035 F \r\n current in the network I = V_m/z = V_m/squareroot R^2 + (x_c - x_L)^2 given V_in = 0.5 V_Rms V_in = 0.5 V_m/squareroot 2 = V_m/2 squareroot 2 I = V_in times 2 squareroot 2/squareroot 20^2 + (1000.035 - 999.96)^2 I = 0.13 V_in = 0.143v_in c) voltage drop across capacitor V_c = V_in times 0.01 mu F/20