An LC circuit consists of a 3.00 mH inductor and a 5.00 AF capacitor. (a) Find i

Question

An LC circuit consists of a 3.00 mH inductor and a 5.00 AF capacitor. (a) Find its impedance at 60.0 Hz Find its impedance at 10.0 kHz. (b) Compare these values of Z with those found in Example 22.12 of the textbook, in which there was also a resistor. Why are they similar? (Select all that apply.) O At low frequency, the inductor dominates. O At high frequency, the inductor dominates. O At high frequency, the capacitor dominates. O The resistor makes little contribution to the total impedance. O At low frequency, the capacitor dominates.

Explanation / Answer

impedance Z = sqrt(sqr((Xl - Xc) ))

Xl = omega * l = 2pi * 60 * 3 * 10^-3 = 1.13

Xc = 1/(omega*C) = 1/ (2pi*60* 5 * 10^-6) = 530.78

Z = 529.65 ohm

for f = 10000 Hz

impedance Z = sqrt(sqr((Xl - Xc) ))

Xl = omega * l = 2pi * 10000 * 3 * 10^-3 = 188.4

Xc = 1/(omega*C) = 1/ (2pi*10000* 5 * 10^-6) = 3.18

Z = 185.22 ohm

2)

the resonance condition

omega = 1/sqrt(l*C)

2pi * 3 * 10^9 = 1/sqrt(8 * 10^-9 * C)

C = 0.35 pF

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