ABSTRACT
We saw in Section 4.6 of Chapter 4 that the equations for voltage and current for capacitors are
) )( (=i t C dv t dt
; 1
0∫( ) ( )= +v t C i t dt v and in Section 4.6 for inductors
( ) ( )=v t L di t dt
; 1
0∫( ) ( )= +i t L v t dt i Such equations depend on time, which is the domain of our functions. However, thanks to a mathematical tool, an integral transform, it is possible
to change the domain of functions and operate not in time but in frequency or, more generically, in the domain of the complex argument s by the Laplace transform, denoted L f t{ }( ) . In such a way, the equations of capacitors and inductors are no longer given by derivatives and integrals, which can be difficult to treat mathematically, but become easy expressions of the type v = Xi, in which X is named reactance.
