An LC circuit consists of a 2.80 mH inductor and a 5.04 µF capacitor. (a) Find i

Question

An LC circuit consists of a 2.80 mH inductor and a 5.04 µF capacitor.

(a) Find its impedance at 58.2 Hz.

_____ ?
(b) Find its impedance at 11.3 kHz.
_____ ?

(c) Now a 30.1 ? resistor is added in series with the inductor and capacitor. Find the impedance of this RLC circuit at 58.2 Hz and 11.3 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.)

a. At high frequency, the capacitor dominates.

b. The resistor makes little contribution to the total impedance.

c. At high frequency, the inductor dominates.

d. At low frequency, the capacitor dominates.

e. At low frequency, the inductor dominates.

Explanation / Answer

a) impedance in LC circuit is z = XC-XL

XC = 1/WC

XL = WL

w = 2pif

z = 1/2*3.14*58.2*5.04*10^-6-2*3.14*58.2*0.0028 = 541.6 ohm ohm

b) z = 1/2*3.14*11.3*1000*5.04*10^-6-2*3.14*11.3*1000*0.0028 = 196 ohm

c) in a RLC circuit

z = sqrt(R^2+(XL-XC)^2)

for f = 58.2 Hz

z = 542.4 ohm

for 11.3 k Hz

z = 198.3 ohm

d) resistor makes littele contribution to the resistance

at high frequency XL dominates that is 2pif*L

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