Hi all. I'm trying to do a circuit problem in my book. The circuit consists of a resistor, capacitor, inductor and a voltage source all in series. The first part of the question says: Find the resonance frequency and half-power frequencies. My book does go on and solve this problem with two different methods using given formulas for series RLC circuits, however, I would like to solve this circuit without formulas (if possible). My problem is calculating the half-power frequency not the resonance frequency. Given: R = 2 Ohms L = 1 mF C = .4 microH My approach: Transfer function: H(s) = R + sL + 1/sC => H(ω) = j(ω*R*C) + (1 - [ω^2 * L * C]) Magnitude of Transfer function: |H(ω)| = √( (ω*R*C)^2 + (1 - [ω^2 * L * C])^2 ) Set Magnitude of Transfer function equal to 1/√2 or set Magnitude of Transfer function squared equal to 1/2: |H(ω)| = 1/√2 or |H(ω)|^2 = 1/2 Solving for this I get ω1 = -27k or ω2 = -65k Obviously this is wrong due to the negative ω's. Not only is the sign wrong but also the magnitude. The book achieved the answers: ω1 = 49k or ω2 = 51k Can anyone please tell me what I'm doing wrong (don't tell me to use formulas please)? Thank you for your time. PS: This is NOT a homework problem.