Series & parallel
Series and parallel are the two ways components combine, and each comes with a guarantee. In series, parts form one path, so the same current flows through every one of them. It has nowhere else to go. The voltages across them add up, and series resistances simply sum: 1 kΩ + 2 kΩ behaves as 3 kΩ.
In parallel, parts share the same two nodes, so each one sees the same voltage, and the currents through them add. Every added parallel path makes current flow easier, so the total resistance drops below the smallest branch. Two equal resistors in parallel give half the resistance of one.
These guarantees double as debugging tools. Old Christmas lights are the standard example: one series bulb fails open and the whole string goes dark, because the only path is broken. If one parallel branch opens instead, the rest keep working at full voltage. Recognizing which topology you’re looking at tells you what a failure will do and where to put your probes.
Key points
- Series: one path, identical current through all parts. Voltages add and resistances add.
- Parallel: shared nodes, identical voltage across all parts, and the currents add.
- Parallel resistance is always below the smallest branch. Two equal resistors halve it.
- An open in series kills the whole chain. An open in parallel only kills its own branch.
Practice
0 of 4 answered · Not startedWrong answers just let you try again, and hints are there if you want them. Answering every question first time, without hints, is what earns mastery.
- 1
Two 1 kΩ resistors are connected in parallel. What is the equivalent resistance?
- 2
What is shared by every component in a series path?
- 3
Three 300 Ω resistors are connected in parallel. What is the equivalent resistance?
Ω - 4
A 470 Ω and a 220 Ω resistor sit in series. What is the total resistance?
Ω
