(15%) Problem 3: A series AC circuit contains a voltage source, a resistor, a ca

Question

(15%) Problem 3: A series AC circuit contains a voltage source, a resistor, a capacitor, and an inductor. The voltage source supplies the voltage v = V0 sin(ot), where 70 = 55 V, and = 55 rad/ s. The components' values are R = 41 , C = 0.062 F, and L = 1.9H 17% Part (a) Calculate the capacitive reactance of the circuit, in ohms Grade Summa Deductions Potential 0% 100% sin0 7 8 9 cosO cotanasin acosO atan acotansinh coshOtanh0 cotanh0 O Degrees Radians tan Submissions tempts remaining: 10 (5% per attempt) detailed view END NO DELI CLEAR Submit Hint I give up! Hints: 2% deduction per hint. H ints remaining: 2 Feedback: 0% deduction per feedback. - 17% Part (b) Find the inductive reactance of the circuit, in ohms - - 17% Part (f) Find the average power delivered to the circuit, in watts 17% Part (c) Calculate the circuit's impedance, in ohms 17% Part (d) Find the maximum current in the circuit. In amperes 17% Part (e) Calculate the rms current in the circuit, in amperes

Explanation / Answer

a)

Inductive reactance

XL=WL =55*1.9 =104.5 ohms

b)

Capacitive reactance

XC=1/WC=1/55*0.062 =0.293 ohms

c)

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[412+(104.5-0.293)2]

Z=111.98 ohms =112 ohms

d)

Maximum current

Imax=Vo/Z=55/112=0.491 A

e)

rms current is

Irms=0.491/sqrt(2)=0.3473 A

f)

Average power

Pav=Irms2R =0.34732*41=4.945 watts

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