Definition of Current

i=dqdt, (1.2)
where
i=the current in amperes, q=the charge in coulombs, t=the time in seconds.


Equations 1.1 and 1.2 define the magnitude of voltage and current,
respectively. The bipolar nature of electric charge requires that we assign
polarity references to these variables.
current is made up of discrete moving electrons, we do not need to
consider them individually because of the enormous number of them. Rather,
we can think of electrons and their corresponding charge as one smoothly
flowing entity. Thus, i is treated as a continuous variable.
One advantage of using circuit models is that we can model a component
strictly in terms of the voltage and current at its terminals. Thus, two
physically different components could have the same relationship between
the terminal voltage and terminal current. If they do, for purposes of circuit
analysis, they are identical. Once we know how a component behaves at its
terminals, we can analyze its behavior in a circuit. However, when
developing component models, we are interested in a component’s internal
behavior. We might want to know, for example, whether charge conduction
is taking place because of free electrons moving through the crystal lattice
structure of a metal or whether it is because of electrons moving within the
covalent bonds of a semiconductor material. These concerns are beyond the
realm of circuit theory, so in this book we use component models that have
already been developed.