Answer:
[tex]f=\frac{1}{2\pi \sqrt{LC}}[/tex]
Explanation:
We know that impedance of a RLC circuit is given by [tex]Z=R+J(X_L-X_C)[/tex]
So [tex]Z=\sqrt{R^2+(X_L-X_C)^2}[/tex] here R is resistance [tex]X_L[/tex] is inductive reactance and [tex]X_C[/tex] is capacitive reactance
To minimize the impedance [tex]X_L-X_C[/tex] should be zero we know that [tex]X_L=\omega L\ and \ X_C=\frac{1}{\omega C}[/tex]
So [tex]\omega L-\frac{1}{\omega C}=0[/tex]
[tex]\omega ^2=\frac{1}{LC}[/tex]
[tex]\omega =\sqrt{\frac{1}{LC}}[/tex]
We know that [tex]\omega =2\pi f[/tex]
So [tex]\omega =2\pi f=\frac{1}{\sqrt{LC}}[/tex]
[tex]f=\frac{1}{2\pi \sqrt{LC}}[/tex]
Where f is resonance frequency
