If the components of the circuit are connected in one single path is it termed as series. The same current would flow through all the components while the voltage would differ from one component to another. For example you have lit three lamps in series to the same power source, the first one would receive more voltage than the last.
For DC signals, the linearity of the system implies that H is independent of Vin. For dynamic signals, the transfer function cannot in general be described simply. However, if the input is a sinusoidal signal then the output must also be a sinusoidal signal with the same frequency but possibly a different amplitude and phase. In other words, a linear system can only modify the amplitude and phase of a sinusoidal input.
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