Why analysis method circuit such as: Mesh, Nodal analysis, superposition, in electrical circuit can be apply in phasor domain
It's really problem when I study AC circuit in electrical circuit. I don't know it clearlyWhat is the actual homework problem you are being asked?
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When you mention to Laplace transform and linear circuit. I really think that I need to do. Thank sirGo back and look at the development of the phasor technique. Go through the same process that was used to find the current through a resistor that is being powered by a voltage source. Go through the same process that was used to combine two resistors, capacitors, or inductors that are in series or parallel.
Then, to really see the beauty of it, go through the process of finding the current in a capacitor or an inductor connected to an AC voltage source (in steady state). Solve the differential equation and compare this to using phasors. Then do the same for a series RC circuit. At that point you should be a true believer.
Linear circuits are described by linear differential equations. One technique that can be used to solve such equations are Laplace transforms, which turn a differential equation into an algebraic equations, that are then solved using the normal techniques that apply to systems of linear equations, and then the result is transformed back into the time domain.
When you write the phasor form of a sinusoidal signal or the complex impedance of a capacitor or inductor, all you are really doing is taking the Laplace transform of it.