An LC circuit consists of a 3.15 mH inductor and a 5.19 µF capacitor. (a) Find i

Question

An LC circuit consists of a 3.15 mH inductor and a 5.19 µF capacitor.

(a) Find its impedance at 57.9 Hz.

(b) Find its impedance at 11.2 kHz.

(c) Now a 33.5 resistor is added in series with the inductor and capacitor. Find the impedance of this RLC circuit at 57.9 Hz and 11.2 kHz

At 11.2 kHz

(d) Compare the values of Z in parts (a) and (b) with those found in part (c), in which there was also a resistor. Why are they similar? (Select all that apply.)

At low frequency, the capacitor dominates.

At high frequency, the inductor dominates.

At low frequency, the inductor dominates.

At high frequency, the capacitor dominates.

The resistor makes little contribution to the total impedance.

Explanation / Answer

Given

Inductance L = 3.15 mH = 3.15 x 10-3 H
Capacitance C = 5.19 µF = 5.19 x 10-6 H

Resistance R = 33.5 ohm

Solution

a)

The inductive reactance XL = 2fL

XL = 2 x 3.14 x 57.9 x 3.15 x 10-3

XL = 1.14 ohm

The Capacitive Reactance XC = 1/2fC

XC = 1/2 x 3.14 x 57.9 x 5.19 x 10-6

XC = 530 ohm

The impedance of the circuit

Z = {|(XL - XC)2|}1/2

Z = {|(1.14-530)2|}1/2

Z = 528.86 ohm

b)

The inductive reactance XL = 2fL

XL = 2 x 3.14 x 11.2 x103 x 3.15 x 10-3

XL = 221.6 ohm

The Capacitive Reactance XC = 1/2fC

XC = 1/2 x 3.14 x 11.2 x103 x 5.19 x 10-6

XC = 2.74 ohm

The impedance of the circuit

Z = {|(XL - XC)2|}1/2

Z = {|(221.6-2.74)2|}1/2

Z = 218.86 ohm

C)

The impedance of the circuit when f = 57.9 Hz

Z = {R2 + (XL - XC)2}1/2

Z = {(33.5)2+|(1.14-530)2|}1/2

Z = 529.9 ohm

The impedance of the circuit when f = 11.2 kHz

Z = {R2 + (XL - XC)2}1/2

Z = {(33.5)2+|(221.6-2.74)2|}1/2

Z = 221.4 ohm

D)

At low frequency, the capacitor dominates. Because the reactance of capacitor is inversely proportional to the frequency

At high frequency, the inductor dominates. Because the reactance of the inductor is directly proportional to the frequency

The resistor makes little contribution to the total impedance. The resistor have very little value comparing to the reactance of other elements. so it do not make much change to the total impedance

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