Definition of Operational Impedance

Analysis of Eqs. (2.84), (2.86), and (2.87) reveals that the relation between current and potential in the presence of resistance, capacitance, and inductance may be represented in a general form  

The operational impedance is the ratio of the Laplace transform of the potential to the Laplace transform of the current (Eq. 2.88). It is usually used for an arbitrary perturbation signal. For the periodic signal it is equivalent to the definition using Fourier transformation. What follows are examples of the applicatirMi of the Laplace technique to the determinatirHi of the current-potential relations and the impedances. 

Example 2.10 Determine the current after application of the potential step E(fj(f) [see Fig. 2.5 for a definition of the Heaviside function rj t) and its transform] to the connection of the resistance, R, and capacitance, C, in series. 

The system is described by Eq. (2.84). The transform of the potential step Eq rjif) is 

An inverse Laplace transform using Eq. (2.26) gives the solution in the time domain  

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