Question

ろ 100 Loo

Find Vth, Zth, In

Answer 1

Given circuit omega = 2 middot pi middot 2000 Find Z_th, V_th, I_N (i) To find Z_th across a & b Represent the above circuit, voltage and current sources with their internal Impedances. Voltage Source-Short circuit Current Source-open circuit j omega L, -j 1/omega C Equivalent Reactances of Inductance & Capacitance X_L = j 2 times pi times 2000 times 33 times 10^-3 = j414.690 Ohm X_C = -j 1/ 2 times pi times 2000 times 330 times 10^-12 = -j241143.8 Ohm X_L Parallel to X_C = j 414.6 - j (241143.8)/-j241143.8 + j414.6 = 414.6 middot (241143.8)/-j 240728.4 = j415.31 Z_th = 100 + j415.31 (ii) To find V_th Voltage across the Capacitor is equal to the Voltage across the a & b. Since the Current through the Resistance is zero X_L = j414.690 Ohm X_C = -j241143.8 Ohm Applying the voltage divider Rule Voltage across Capacitor V_ab = 80e^j80 middot X_C /X_L + X_C = 80 middot e^80 (-j241143.8)