Question

Obtain the resonant frequency ω_r 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?

Answer 1

Inductance, L = 2.0 H

Capacitance, C = 32 μF = 32 × 10⁻⁶ F

Resistance, R = 10 Ω

Resonant frequency is given by the relation,

ω_r = `1/sqrt"LC"`

= `1/sqrt(2 xx 32 xx 10^-6)`

= `1/(8 xx 10^-3)`

= 125 s⁻¹

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

`"Q" = 1/"R" sqrt ("L"/"C")`

= `1/10 sqrt(2/(32 xx 10^-6))`

= `1/10 xx 1/(4 xx 10^-3)`

= 25

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