Question

The expression for lower half power frequency is?

(a) (-R+√(x^2+4LC))/4πL

(b) (–R-√(x^2+4LC))/4πL

(c) (R-√(x^2+4LC))/4πL

(d) (R+√(x^2+4LC))/4πL

I had been asked this question in an international level competition.

My doubt stems from Bandwidth of an RLC Circuit in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct answer is (a) (-R+√(x^2+4LC))/4πL

To explain: Selectivity indicates how well a resonant circuit responds to a certain frequency and eliminates all other frequencies. At lower power frequency, XC > XL(1/2πf1C)-2πf1L=R. f1 = (-R+√(x^2+4LC))/4πL.