A 220 ohm resistor, 0.400 H inductor, 6.00 microF capacitor, and voltage source

Question

A 220 ohm resistor, 0.400 H inductor, 6.00 microF capacitor, and voltage source of amplitude 30.0 V and angular frequency 230 rad/s are connected to form an L-R-C series circuit.

(a) What is the impedance of the circuit?

(b) What is the current amplitude?

(c) What is the phase angle of the source voltage with respect to the current?

(d) What are the voltage amplitudes across the resistor, inductor, and capacitor?

(e) Explain how it is possible for the voltage amplitude across the capacitor to be greater than the voltage amplitude across the source.

Explanation / Answer

230 rad/s==>L=0.4 H==>C=6 uF==>R=220 ohms==>Vsource=30 V

a) XL=230*0.4=92 ohms==>XC=1/(230*6E-6)=724.64 ohms

Z=sqrt(R^2+(XL-XC)^2)=669.8 ohms

b) 30 V/669.8 ohms=44.8 mA

c) arctan((XL-XC)/R)=-70.8 degrees

d) VR=0.0448*220=9.854 V

VL=0.0448*92=4.121 V

VC=0.0448*724.64=32.46 V

e) sqrt(9.854^2(4.121-32.46)^2)=30 V that is equal to source

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.