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RLC Circuits and Resonance - Technical MCQs

Q1:

The output voltage at the resonant frequency is _____ in the given circuit.

A 0 V

B 557 mV

C 6.08 V

D 6.5 V

ANS:C - 6.08 V

You can get the Vout via the total impedance of the parallel LC tank. To get the output impedance, first, you need to determine the resonant frequency.

1. Equate XC=XL ; 1/(2*6800pF*fr) = 2 *5.8mH*fr ; fr = 25342.62974 Hz.

2. Find XC = XL; XL = 2*5.8mH*25.3416kHz = 923.5481452 ohms = XC.

3. Determine the total impedance of the tank circuit.
Find the Q: Q= XL/Rw = 923.5481/75 = 12.313975,
with Q you can solve for Z, where Z=Rw(1+Q^2).
Z = (75)(1+(12.314)^2) = 11447.549 ohms.

4. Using voltage divider we can now determine for Vo:

Vo = (Vs*Z)/(Z+Rs) = (6.5)*(11447.549)/(11447.549 + 800),
Vo = 6.075425255 V.