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Question

Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0 H, C = 32 μF and R = 10 Ω. What is the Q-value of this circuit?

Solution
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Given: The inductance in the circuit is 2.0H.
The capacitance in the circuit is 32μF.
The resistance in the circuit is 10Ω.

To find: The resonant frequency and Q-value of the circuit.

The resonant frequency is given by
ωr=1LC=12×32×106

125rad/s
The Q value of the circuit is given by:
Q=1RLC=110232×106

Q=25

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