An LC circuit consists of a 2.87 mH inductor and a 4.85 µF capacitor. (a) Find i

Question

An LC circuit consists of a 2.87 mH inductor and a 4.85 µF capacitor.

(a) Find its impedance at 56.1 Hz.


(b) Find its impedance at 12.0 kHz.


(c) Now a 35.2 resistor is added in series with the inductor and capacitor. Find the impedance of this RLC circuit at 56.1 Hz and 12.0 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 high frequency, the capacitor dominates.At low frequency, the capacitor dominates.At low frequency, the inductor dominates.The resistor makes little contribution to the total impedance.At high frequency, the inductor dominates.

Explanation / Answer

given that C=4.85 uF
L=2.87 mH

capacitive impedance=Xc=-j/(2*pi*frequency*C)
inductive impedance=Xl=j*2*pi*f*L

net impedance=Xc+Xl

a)at f=56.1 Hz, Xc=-j584.94 ohms
Xl=j1.0116 ohms

so net impedance=-j583.92 ohms

b)f=12000 Hz
Xc=-j2.734 ohms
Xl=j216.39 ohms

net impedance=Xc+Xl=j213.658 ohms

c)
at 56.1 Hz, net impedance=35.2-j583.92 ohms

magnitude=584.98 ohms

at 12 kHz , net impedance=35.2+j213.658 ohms

magnitude=216.538 ohms

d) at high frequency, inductor dominates.

at low frequency capacitor dominates.

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