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

Inductance, L = 2.0 H

Capacitance, C = 32 μF = 32 x 10^-6 F

Resistance, R = 10Ω

Resonant frequency is given by the relation,

ω_{r= 1/ √ (LC) = 1/ √ (2 x 32 x 10^-6 ) = 1/(8 x 10⁻³ ) = 125 rad/s}

Now ,Q-value of the circuit is given as :

Q = 1/R_√ (L/C) = (1/10) x _{√[2/(32 x 10^-6 ) ]}

= 1/(10 x 4 x 10⁻³ ) = 25

Hence, the Q-Value of this circuit is 25.