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.