I wanted you to explain it to me so I could better understand what is it you don t understand What you ve explained to me above is incorrect and demonstrates that you don t understand impedance or the relationship between phasors and the s domain or even the relationship between the s domain and the time domain I actually thought I had expained some of this rather well in my lengthy post above However either I failed to do so or you didn t bother to try to understand what I wrote I ll close by individually addressing some of the things you said above phasors require a constant frequency which doesn t work for any arbitary wavefunction Yes a phasor is associated with a particular frequency but that in no way implies that phasors can not be used for arbitrary waveforms And setting omega to 0 after time 0 gives you an impedance of infinity which is obviously incorrect except at t This sentence is not even wrong it is meaningless And the impedance for the capacitor does depend on the input however it doesn t depend on the s domain version of the input which makes s domain impedance more useful Again not even wrong At best this statement can be described as confused As for the significance of s I m not an expert in laplace tranforms but s is a parameter that can be related to the frequency of the input How can this be As you ve already correctly stated 1 sC is independent of the input signal One can substitute j for s and find the frequency response This is the closest you came to demonstrating some understanding of this subject It s not quite a correct statement but it s not far off The s domain is better than phasors for handling the unit impulse because phasors require a constant frequency and laplace transformations don t Yeah you ve said this before no matter how many times you say it the fact that it is wrong is not going to change Now that I understand the depth of you misunderstanding I ll be reviewing your edits much more closely