Question

Obtain an expression for the resonant frequency (f₀) of a series LCR circuit.

Answer 1

For a series LCR circuit, resonance occurs when X_L = X_C.

If f₀ is the resonant frequency, then,

2 π f₀ L = `1/(2 pi f_0 C)`

or `f_0^2 = 1/(4 pi^2 L C)`

⇒ f₀ = `1/(2 pi sqrt(LC))`