What is a series-parallel circuit?
With simple series circuits, all components are connected
end-to-end to form only one path for electrons to flow through the
circuit:
With simple parallel circuits, all components are connected
between the same two sets of electrically common points, creating
multiple paths for electrons to flow from one end of the battery to
the other:
With each of these two basic circuit configurations, we have
specific sets of rules describing voltage, current, and resistance
relationships.
- Series Circuits:
- Voltage drops add to equal total voltage.
- All components share the same (equal) current.
- Resistances add to equal total resistance.
- Parallel Circuits:
- All components share the same (equal) voltage.
- Branch currents add to equal total current.
- Resistances diminish to equal total resistance.
However, if circuit components are series-connected in some parts
and parallel in others, we won't be able to apply a single
set of rules to every part of that circuit. Instead, we will have to
identify which parts of that circuit are series and which parts are
parallel, then selectively apply series and parallel rules as
necessary to determine what is happening. Take the following
circuit, for instance:
This circuit is neither simple series nor simple parallel.
Rather, it contains elements of both. The current exits the bottom
of the battery, splits up to travel through R3 and R4,
rejoins, then splits up again to travel through R1 and R2,
then rejoins again to return to the top of the battery. There exists
more than one path for current to travel (not series), yet there are
more than two sets of electrically common points in the circuit (not
parallel).
Because the circuit is a combination of both series and parallel,
we cannot apply the rules for voltage, current, and resistance
"across the table" to begin analysis like we could when the circuits
were one way or the other. For instance, if the above circuit were
simple series, we could just add up R1 through R4
to arrive at a total resistance, solve for total current, and then
solve for all voltage drops. Likewise, if the above circuit were
simple parallel, we could just solve for branch currents, add up
branch currents to figure the total current, and then calculate
total resistance from total voltage and total current. However, this
circuit's solution will be more complex.
The table will still help us manage the different values for
series-parallel combination circuits, but we'll have to be careful
how and where we apply the different rules for series and parallel.
Ohm's Law, of course, still works just the same for determining
values within a vertical column in the table.
If we are able to identify which parts of the circuit are series
and which parts are parallel, we can analyze it in stages,
approaching each part one at a time, using the appropriate rules to
determine the relationships of voltage, current, and resistance. The
rest of this chapter will be devoted to showing you techniques for
doing this.
- REVIEW:
- The rules of series and parallel circuits must be applied
selectively to circuits containing both types of interconnections.
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