A 1.8-H inductor and a 3.5 µF capacitor are connected in series with a 45 resist

Question

A 1.8-H inductor and a 3.5 µF capacitor are connected in series with a 45 resister, and the combination is connected to an AC generator supplying 21 V peak at 65 Hz.

(a) At the instant the generator voltage is at its peak, what is the instantaneous voltage across the resistor?

(b) At the instant the generator voltage is at its peak, what is the instantaneous voltage across the capacitor?

(c) At the instant the generator voltage is at its peak, what is the instantaneous voltage across the inductor?

(d) If an rms voltmeter is connected across the inductor, what will it read?

(e) If an rms voltmeter is connected across the capacitor, what will it read?

(f) If an rms voltmeter is connected across the resistor, what will it read?

Explanation / Answer

Inductive reactance

XL=2pifL=2pi*65*1.8=735.13 ohms

Capactive reactance

XC=1/2pifC =1/2pi*65*(3.5*10-6) =699.58 ohms

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[452+(735.13-699.58)2]

Z=57.35 ohms

Phase angle

o=tan-1(XL-Xc/R) =tan-1(735.13-699.58/45) =38.31o

Peak current flowing in the circuit

IP=V/Z=21/57.35=0.366 A

Peak voltage across each element

VRp=I*R=0.366*45=16.47volts

VLp=IXL=0.366*735.13=269.06 volts

Vcp=IXc=0.366**699.58 =256.05 volts

a)

VR=16.47Sin(90-38.31) =12.9 Volts

b)

VC=256.05Sin(-38.31) =-158.7 Volts

c)

VL=269.06Sin(180-38.31) =166.8 Volts

d)

VLrms=269.06/sqrt(2)=190.25 Volts

e)

VCrms=256.05/sqrt(2)=181.05 volts

f)

VRrms=16.47/sqrt(2)=11.65 Volts

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