3. A resistor, capacitor and inductor are connected in series to an ac source wi

Question

3.    A resistor, capacitor and inductor are connected in series to an ac source with a frequency of 30 Hz and an rms potential of 40 V. The resistor has a value of 200 ohms, the inductor has a value of 4.0 H and the capacitor has a value of 6.5 microF.

a.    Calculate XL, XC, phase angle, Z and Irms for this circuit. Does the circuit potential lead or lag the current?

b.    Sketch the phasor diagram for this circuit. Label all vectors and angles.

c.    What is the resonance frequency for this circuit?

d.    What is the rms potential across the capacitor?

Explanation / Answer

a) XL=2*pi*f*L=240*pi=753.98 ohms

XC=1/(2*pi*f*C)=816.179 ohms

arctan((XL-XC)/R)=-17.275 degrees

Z=sqrt(R^2+(XL-XC)^2)=209.45 ohms

Irms=40 V/209.45 ohms=190.98 mA rms

b) I could not get this to diagram

c) fr=1/(2*pi*sqrt(L*C))=31.213 Hz

d) VC=XC*190.98 mA=155.87 volts rms

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