How components connect decides how current, voltage and resistance behave. Learn the formulas, then see them in bulbs, outlets, LED strings and battery packs.
| Series | Parallel | |
|---|---|---|
| Paths for current | One | Several branches |
| Current | Same through every part | Splits between branches |
| Voltage | Splits between parts | Same across every branch |
| Total resistance | Adds up | Drops below the smallest |
| If one part fails | Whole circuit stops | Other branches keep working |
Series resistors share a single path, so their values simply add:
Three resistors of 100 Ω, 220 Ω and 330 Ω in series, connected to a 9 V battery.
R = 100 + 220 + 330 = 650 Ω
I = 9 / 650 ≈ 13.8 mA (the same through all three)
Each added branch gives current another route, so total resistance falls:
100 Ω and 220 Ω in parallel, using the two-resistor shortcut:
R = (100 × 220) / (100 + 220) = 68.75 Ω
Notice 68.75 Ω is below 100 Ω, the smaller resistor. That always happens in parallel.
Three 300 Ω resistors in parallel:
R = 300 / 3 = 100 Ω
Real circuits combine both. Solve them in steps: collapse each parallel group to one value, then add the series parts. Take a 100 Ω resistor in series with a 220 Ω and 330 Ω pair in parallel, on a 12 V supply.
Step 1. Parallel pair:
(220 × 330) / (220 + 330) = 132 Ω
Step 2. Add the series resistor:
Rtotal = 100 + 132 = 232 Ω
Step 3. Total current:
I = 12 / 232 ≈ 51.7 mA
Step 4. Voltage across each part:
100 Ω: 0.0517 × 100 ≈ 5.17 V | parallel pair: 0.0517 × 132 ≈ 6.83 V
The two voltages add back to 12 V, which confirms the answer.
Cells follow similar rules. Take four AA cells, each 1.5 V and 2000 mAh:
| Arrangement | Voltage | Capacity |
|---|---|---|
| 4 in series | 6 V | 2000 mAh |
| 4 in parallel | 1.5 V | 8000 mAh |
| 2 series × 2 parallel | 3 V | 4000 mAh |
Only combine cells of the same type, age and charge level, otherwise stronger cells push current into weaker ones.
Try each one before you open the answer.
R = 1000 / 2 = 500 Ω.
47 + 68 + 100 = 215 Ω.
R = (10 × 40) / 50 = 8 Ω, so I = 8 / 8 = 1 A.
In a series circuit components share one path, so the same current flows through all of them. In a parallel circuit components sit on separate branches, so each branch gets the same voltage.
Each extra branch gives current another path to flow, so the total opposition to flow drops. Two 100 Ω resistors in parallel give 50 Ω.
Parallel wiring gives every device the full supply voltage, and one device switching off does not stop the others.
The circuit breaks and every bulb in the string goes out. In a parallel arrangement, only the failed branch stops working.
Skip the arithmetic. Enter your resistor values and get the total instantly. New to the basics? Start with our Ohm's Law guide.
Open the Series / Parallel Calculator