Resistor Networks & Voltage Divider
Combine resistors in series or parallel and see the current and power in each one — or design a voltage divider and solve for any of its four values.
How do Resistors Combine?
In series the same current flows through every resistor, so their resistances simply add up. In parallel every resistor gets the full voltage and the currents add up, so the total resistance is always smaller than the smallest one.
A voltage divider — two resistors in series — produces a fraction of the input voltage at the point between them. It is used to read sensors, set reference levels and scale signals down for a microcontroller.
Circuit Diagram
seriesResistor Colour Code
| Colour | Digit | Multiplier |
|---|---|---|
| Black | 0 | ×1 |
| Brown | 1 | ×10 |
| Red | 2 | ×100 |
| Orange | 3 | ×1 k |
| Yellow | 4 | ×10 k |
| Green | 5 | ×100 k |
| Blue | 6 | ×1 M |
| Violet | 7 | ×10 M |
| Grey | 8 | — |
| White | 9 | — |
| E12 values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 (× powers of ten) | ||
Key Relations
“Product over sum” — the quick formula for exactly two resistors. For more, add the reciprocals.
Choose R₂, then calculate R₁ and round to a standard value. Keep the resistances high enough to limit wasted current.
Anything connected to Vout is in parallel with R₂ and pulls the voltage down. Make Rload at least ten times larger than R₂.
Sources & Verification
- A. R. Hambley, Electrical Engineering: Principles and Applications, 7th ed., Pearson, 2018 — Ch. 2 (Resistive Circuits: resistances in series and parallel, voltage dividers) and App. B (Nominal Values and the Color Code for Resistors).