Question

2.2kn 10nF Fig. 1. Resistive-capacitive circuit for learning how to measure magnitude and phase shift. 1. Hand Calculations (in a manner suitable for submission) For the circuit in Fig. 1 with f = 7.2 kHz and a source t) = 1.0 cos (Zrf-t|v applied at the circuit input (between points A and D), calculate by hand the voltage vi(t) at the input and the voltage v2(t) at the output (between points B and D).

Answer 1

V_in (t) = 1 middot Cos (2 pi ft) f = 7.2 kHz Consider Impedance network for capacitor, X_C = 1/2 pi fC X_C = 1/2 pi times 7.2 times 10^3 times 10 times 10^-9 X_C = 2.2 k Ohm Apply Voltage division, V_0 = V_1 * (-j X_C)/R - j X_C = 1 * (j 2.2)/2.2 - j 2.2 = 0.7071 angle -45 degree then, V_0 = 0.7071 middot cos (2 pi times 7.2 times 10^3 t - 45 degree)