A series RLC circuit has R = 420 ?, L = 1.30 H, C = 3.7 F. It is connected to an

Question

A series RLC circuit has R = 420 ?, L = 1.30 H, C = 3.7 F. It is connected to an AC source with f = 60.0 Hz and ?Vmax = 150 V.

What if the frequency is now increased to f = 86 Hz, and we want to keep the impedance unchanged?

?VR =___ V ?VL =___V
?VC =____V A series RLC circuit has R = 420 ?, L = 1.30 H, C = 3.7 F. It is connected to an AC source with f = 60.0 Hz and ? V max = 150 V. What if the frequency is now increased to f = 86 Hz, and we want to keep the impedance unchanged? (A) What new resistance should we use to achieve this goal? R = ? (B) What is the phase angle (in degrees) between the current and the voltage now? phi = (C) Find the maximum voltages across each element.

Explanation / Answer

at f=60 Hz

Capacitive reactance

Xc=1/2pifC =1/2pi*60*(3.7*10-6) =716.9 ohms

Inductive reactance

XL=2pifL=2pi*60*1.3 =490.1 ohms

impedance

Z=sqrt[R2+(XL-Xc)2]=sqrt[4202+(490.1-716.9)2]

Z=477.3 ohms

at f=86 Hz

Capacitive reactance

Xc=1/2pi*86*(3.7*10-6) =500.2 ohms

Inductive reactance

XL=2pi*86*1.3= 702.5 ohms

Impedance

ZN=sqrt[R2+(XL-Xc)2]=sqrt[R2+(702.5-500.2)2]

Given ZN=Z

477.3=sqrt[R2+40925.3]

R=432.3 ohms

b)

Phase angle

o=tan-1(XL-Xc/R) =tan-1(702.5-500.2/432.2)

o=25.1o

c)

Maximum current flowing in the circuit

Imax=Vmax/Z =150/477.3 =0.3143 A

Voltage across each element

VR=Imax*R =0.3143*432.3 =135.8 Volts

VL=Imax*XL=0.3143*702.5=220.7 Volts

Vc=Imax*Xc=0.3143*500.2=157.2 Volts

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