Question

A curve between I and ω in a series LCR circuit connected to an emf E₀ sin ωt has a peak (I = I₀) at ω = ω₀ (resonance). Suppose ω₁ and ω₂ are two values of ω on both sides of ω₀ at which the value of I is I₀ /√2 . Show that (a) ω₁ and ω₂ are half-power points and ∆ω = ω₂ – ω₁ = R/L, (b) the Quality factor of the circuit is Q = ω₀L/R.

Answer 1

We have

Since power ∝ i², ω₁ and ω₂ correspond to frequencies at which P = P₀/2, where P₀ is the maximum power at resonance.