AP® Physics 2: Algebra-Based · Unit 11 · Topic 11.5
Combination Resistor Networks
A combination network mixes series and parallel resistors. You solve it by collapsing the parallel chunks into single equivalent resistors first, then adding up the series chain, working from the inside out.
A real circuit is rarely pure series or pure parallel. It's usually a mix: some resistors share the same current in a row, others share the same two nodes and split the current between them. To find the total resistance, you work in stages. Find a cluster of resistors that is purely parallel or purely series, collapse it to one number, redraw the circuit with that one resistor in place of the cluster, and repeat. Eventually the whole mess becomes a single equivalent resistance facing the battery.
Once you have that single number, current from the battery is just V divided by R_total, by Ohm's law. That current is the total current leaving the battery, and it has to flow through anything in series with the battery undivided. When it hits a parallel section, it splits between the branches, with more current going through the smaller resistance, then recombines before continuing. Voltage works the opposite way: it's the same across each parallel branch, but splits across resistors in series.
This is why cutting one branch changes everything downstream. Removing a parallel branch raises the resistance of that whole section, which raises the total resistance of the circuit, which lowers the total current the battery pushes out. Any resistor in series with that section dims, because less current now flows through it. But a resistor in a surviving parallel branch next to the cut one can get brighter, because it now carries current that used to be shared with the branch that got removed. This connects directly to how capacitors behave in live circuits: both come down to tracking how current reroutes when the path geometry changes.
Key terms
- equivalent resistance
- The single resistance value that would draw the same current from the battery as the whole network.
- series
- Components arranged so the same current flows through each one in turn, no splitting.
- parallel
- Components arranged across the same two nodes, so they share the same voltage but split the current.
- branch
- One of the separate paths current can take between two shared nodes in a parallel section.
Watch it explained
- How it worksWalk me through collapsing a series-parallel network down to a single equivalent resistance.
- Worked exampleFind the equivalent resistance when a 4 ohm resistor sits in series with parallel 6 and 3 ohm resistors.
- Worked exampleFind the current through each resistor in that same network on a 12 V battery.
- Going furtherWhat happens to the brightness of the other bulbs when one parallel branch is cut open?
Check yourself
End of topic.