Many real networks are neither purely in series nor purely in parallel: they are mixed networks, in which some resistors are in series and others in parallel. To find their equivalent resistance no new method is needed — it suffices to apply the two known rules repeatedly, reducing one group at a time.
Principle — Progressive simplification
One identifies a subset of resistors that is clearly in series or in parallel, replaces it with its equivalent resistance, and obtains a simpler network. Repeating this, the network collapses step by step down to a single equivalent resistor.
The method, in practice:
- Find the innermost group recognisable as pure series or pure parallel (often the branches furthest from the source).
- Replace it with its : if in series, the reciprocal rule if in parallel.
- Redraw the reduced circuit and repeat from step 1.
- Once a single equivalent resistor is reached, the total current from the source is found; then one works back to find the voltages and currents in the individual branches (at each step the voltage of the equivalent group is known).
Recognising series and parallel
Two resistors are in series only if there are no branches between them; they are in parallel only if both their ends coincide with the same two nodes. A typical mistake is calling “in series” resistors that are separated by a node where another branch enters or leaves.
Worked example
A complete example of a mixed network (with and in parallel, then in series with , including the branch currents and the energy check) is worked through step by step among the exercises in this section.
Links
Topics: Circuiti elettrici Concepts: Resistenze in serie e parallelo Skills: Semplificazione di reti
Related exercises: Esercizio svolto — rete mista serie e parallelo · Problema — vero o falso su serie e parallelo · Problema — resistenza equivalente serie-parallelo