A 180 ohm resistor, 0.400 H inductor, 6.00 mu F capacitor, and voltage source of

Question

A 180 ohm resistor, 0.400 H inductor, 6.00 mu F capacitor, and voltage source of amplitude 30.0 V and angular frequency 270 rad/s are connected to form an L-R-C series circuit. What is the impedance of the circuit? ohm What is the current amplitude? A What is the phase angle of the source voltage with respect to the current? Does the source voltage lag or lead the current? They are in phase. lead lag What are the voltage amplitudes across the resistor, inductor, and capacitor? resistor V inductor V capacitor V

Explanation / Answer

Impendece in RLC circuit is given by Z^2 = R^2+(XL-XC)^2

where XL = inductive reactance = WL = 2pifL = 270 * 0.4

XL = 111.6 ohms

Xc = capcacitve reactnace = 1/WC = 1/(2pifC) = 1/(270 * 6*10^-6)

Xc = 617.28 ohms

part A :

Impedence Z^2 = 180^2 + (617.28 - 111.6)^2

Z = 536.76 ohms

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part B :

current I = V/Z

I = 30/536.76

I = 0.0558 AMps or 55.89 mA

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part C:

phase angle tan theta = (XL-Xc)/R

tan theta = (111.6 - 617.28)/180

theta = -70.4 deg

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Volatge lag the current a

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part D :

V across R = IR

Vr = 0.0558 * 180

Vr = 10 V

V across Inductor = iXL

VL = 0.0558* 111.6

VL = 6.22 Volts

V across Capacitor

Vc = i XC

Vc = 0.0558 * 617.28

vc = 34.45 Vols

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