A series RLC circuit contains the following components. The resistance of the ci

Question

A series RLC circuit contains the following components. The resistance of the circuit is
200.0 ohm, the inductance is 230.0 mH, and the capacitance is 70.0 uF. There is a source
with delta Vmax = 36.0 V operating at 60.0 Hz.
Find the following:
Part A (15 pts)
a) The inductive reactance
b) The capacitance reactance
c) The impedance
d) The maximum current
e) The phasor angle
Part B (10 pts)
a) If you could choose a different inductor is it possible that the voltage across the
inductor be greater than the source voltage delta Vmax? Yes or No
b) If no

Explanation / Answer

a)

Inductive reactance

XL=2pi*f*L=2pi*60*0.23=86.7 ohms

b)

Capacitive reactance

XC=1/2pi*60*70*10-6=37.9 ohms

c)

Impedance

Z=sqrt[R2+(XL-XC)2]=sqrt[2002+(86.7-37.9)2]

Z=205.9 ohms

d)

Imax=Vmax/Z =36/205.9 =0.175 A

e)

Phase angle

o=tan-1(XL-XC/R) =tan-1(86.7-37.9/200)

o=13.71o

Part B

a)

Yes

b)

VL>Vmax

IXL>Vmax

(Vmax/Z)XL>Vmax

XL>Z

XL>sqrt[2002+(XL-37.9)2]

XL2>2002+XL2-75.8XL+37.92

41436.41>75.8XL

XL=546.65

2pi*f*L=546.65

L=546.65/2pi*60

L=1.45 H

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