Question

A series AC circuit contains a resistor, an inductor of 220 mH, a capacitor of 4.20 ur, and a source with ΔⅤmax-240 V operating at 50.0 Hz. The maximum current in the circuit is 170 mA. (a) Calculate the inductive reactance 69.11 (b) Calculate the capacitive reactance 757.88 (c) Calculate the impedance 141 (d) Calculate the resistance in the circuit. 6.887 The impedance is a function of the resistance and the impedances of the inductor and capacitor. kΩ (e) Calculate the phase angle between the current and the source voltage Need Help?ReadltTalk to & Tutor Talk to a Tutor

Answer 1

Let consider a series RLC circuit of resistance R, inductance L & capacitance c carries a maximum current I_max = 170 m Amp L = 220 mH, C = 4.2 mu F Let inductive reactance X_L = 2 pi fL, where f is frequency of source X_L = 2 pi times 50 times 220/1000 = 22 pi = 69.115 ohm capacitive reactance X_C = 1/2 pi fc = 1/2 pi times 50 times 4.2 times 10^-6 X_C = 10^4/4.2 pi = 757.88 ohm let Vertical-bar z Vertical-bar be the independent of circuit, by ohm's law Vertical-bar z Vertical-bar = V_max/I_max = 240/170 times 10^-3 = 1.4117 K ohm Impendence z = squareroot R^2 + (X_C - X_L)^2. squareroot R^2 + (757.88 - 69.115)^2 = 1142 ohm squareroot R^2 + 688.77^2 = 1142 = > R^2 = 329759.8871 R = 910.911 ohm = 0.9109 K ohm Phase angle between current and voltage source is theta and tan theta = X_C - X_L/R = 757.88 - 69.115 /910.911 = 688.77/910.911 tan