Question

Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0H, C = 32 µF and R = 10 Ω. What is the Q-value of this circuit?
no non sense answers please​

Answer 1

Answer:

See below.

Explanation:

The resonant frequency for an LCR circuit is given by,

$\omega _0=\dfrac{1}{\sqrt{LC}}$

Substituting the values,

$\omega _{0}=\dfrac{1}{\sqrt{2\times 32\times 10^{-6}}}$

which gives,

$\omega _{0}=\dfrac{1}{8}\times 10^{3} \ rad \ s^{-1}$

The quality factor for the LCR circuit is given by,

$Q=\dfrac{\omega _{0}L}{R}$

Substituting the values,

$\begin{aligned}Q=\dfrac{\dfrac{1}{8}\times 10^{3}\times 2}{10}\\ =0.025\times 10^{3}\\ =25\end{aligned}$