Question

In a series RLC circuit, R=2ohm, L=1mH and C=0.4microfarad.What is resonance frequency in rad/sec? ​

Answer 1

Answer:

please give me some point I have no points

Answer 2

Given :

R = 2 ohm

L = 1 mH = 1 × 10⁻³ H

C = 0.4 μF = 0.4 × 10⁻⁶ F

To Find :

Resonance angular frequency

Solution :

In a resonant LCR circuit, current and EMF are in the same phase.

In purely resistive circuit or resonant LCR circuit, Inductive reactance ($X_L$) is equal to Capacitive reactance ($X_c$). So,

     $X_c$ = $X_L$

⇒  $\frac{1}{Cw_0}$ = Lω₀      

⇒  ω₀ = $\frac{1}{\sqrt{LC} }$

Resonant angular frequency (ω₀) = $\frac{1}{\sqrt{LC} }$

                                                         = $\frac{1}{\sqrt{10^-^3 * 0.4 * 10^-^6} }$

                                                         = $\frac{10^5}{2}$

                                                         = 5 × 10⁴ rad/sec

Therefore, in the given LCR circuit, the value of resonant angular frequency is 5 × 10⁴ rad/sec.