A circuit connects circuit elements together in a specific configuration
designed to transform the source signal (originating from a voltage or current source)
into another signal—the output—that corresponds to the current or
voltage defined for a particular circuit element. A simple resistive circuit is shown
in Figure 1. This circuit is the electrical
embodiment of a system having its input provided by a source system producing
v
in
t
v
in
t
.
To understand what this circuit accomplishes, we want to determine the voltage across
the resistor labeled by its value
R
2
R
2
. Recasting this problem mathematically, we need to solve some set of equations so that
we relate the output voltage
v
out
v
out
to the source voltage. It would be simple—a little too simple at this
point—if we could instantly write down the one equation that relates these two
voltages. Until we have more knowledge about how circuits work, we must write a set of
equations that allow us to find all the voltages and currents that
can be defined for every circuit element. Because we have a three-element circuit, we
have a total of six voltages and currents that must be either specified or determined.
You can define the directions for current flow and positive voltage drop any
way you like. When two people solve a circuit their own ways, the values of
their variables may not agree, but current and voltage values for each element will agree.
Do recall in defining your
voltage and current variables that the v-i relations for
the elements presume that positive current flow is in the same direction as positive
voltage drop. Once you define voltages and currents, we need six nonredundant equations
to solve for the six unknown voltages and currents. By specifying the source, we have
one; this amounts to providing the source's v-i relation. The
v-i relations for the resistors give us two more. We are only halfway
there.
What we need to solve every circuit problem is mathematical statements that express what
the interconnection of elements is. Said another way, we need the laws that govern the
electrical connection of circuit elements. First of all, the places where circuit elements
attach to each other are called nodes. Two nodes are explicitly indicated
in Figure 1; a third is at the bottom where the voltage
source and resistor
R
2
R
2
are connected. Electrical engineers tend to draw circuit diagrams—schematics—
in a rectilinear fashion. Thus the long line connecting the bottom of the voltage source
with the bottom of the resistor is intended to make the diagram look pretty. This line
simply means that the two elements are connected together. Kirchoff's
Laws, one for voltage
and one for current, determine
what a connection among circuit elements means. These laws can help us analyze this circuit.