6) The RLC circuit below is being driven by an AC source with a frequency of 47.

Question

6) The RLC circuit below is being driven by an AC source with a frequency of 47.77 Hz resulting in a maximum current Imax = 0.25 amps.

A) Calculate the impedance of this circuit.

24 ohms

50 ohms

55 ohms

111 ohms

135 ohms

B) Calculate VR the maximum voltage across the resistor.

VR=12.5 V

VR=13.9 V

VR=15.3 V

VR=27.8 V

VR=33.8 V

C)  Calculate VC the maximum voltage across the capacitor.

VC=12.5 V

VC=13.9 V

VC=15.3 V

VC=27.8 V

VC=33.8 V

D)  Calculate VL the maximum voltage across the inductor.

VL=12.5 V

VL=13.9 V

VL=15.3 V

VL=27.8 V

VL=33.8 V

E)  Calculate Vo the maximum voltage across the generator.

Vo=12.5 V

Vo=13.9 V

Vo=15.3 V

Vo=27.8 V

Vo=33.8 V

Explanation / Answer

a)

Inductive reactance

XL=WL =300*0.45=135 ohms

Capacitive reactance

Xc=1/WC =1/300*(30*10-6)=111.11 ohms

Impedance

Z=sqrt[R2+(XL-Xc)2]=sqrt[502+(135-111.11)2]

Z=55.4 ohms=55 ohms (approx)

b)

VR=Imax*R =0.25*50 =12.5 Volts

c)

Vc=ImaxXc=0.25*111.11=27.8 Volts

d)

VL=Imax*XL=135*0.25=33.8 Volts

e)

Vo=Imax*Z=0.25*55.4=13.9 Volts

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