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.
When multiple components are connected in parallel, the voltage drop is the same across all components. When multiple components are connected in series, the total voltage is the sum of the voltages across each component. These two statements can be generalized as Kirchoff’s Voltage Law (KVL), which states that the sum of voltages around any closed loop (e.g. starting at one node, and ending at the same node) is zero.
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