Series and parallel resistors, explained.
Series components share a current, and their voltage drops add to the supply. Parallel branches share a voltage, and branch currents add to the total. Parallel equivalent resistance is less than either individual positive resistance.
The relationship to remember
Key formulas
- Series equivalent resistance
- R = R₁ + R₂ + …
- Same current through every resistor
- Parallel equivalent resistance
- 1/R = 1/R₁ + 1/R₂ + …
- Same voltage across every branch
- Two resistors in parallel
- R = R₁R₂ / (R₁ + R₂)
- “Product over sum”
- Series voltage divider
- V₁ = V · R₁ / (R₁ + R₂)
- Voltage drops add to the supply
- Parallel current divider
- I₁ = I · R₂ / (R₁ + R₂)
- Branch currents add to the total
Worked example
Problem. A 9 V supply is connected to a 30 Ω and a 60 Ω resistor. Find the equivalent resistance and the currents when they are in series, then in parallel.
- Series: R = 30 + 60 = 90 Ω, so I = 9 / 90 = 0.1 A through both resistors.
- Series voltage drops: V₁ = 0.1 × 30 = 3 V and V₂ = 0.1 × 60 = 6 V, which add to 9 V.
- Parallel: R = (30 × 60) / (30 + 60) = 20 Ω, so the total current is 9 / 20 = 0.45 A.
- Parallel branches: I₁ = 9 / 30 = 0.3 A and I₂ = 9 / 60 = 0.15 A, which add to 0.45 A.
Answer. In series: 90 Ω and 0.1 A. In parallel: 20 Ω and 0.45 A in total, split 0.3 A and 0.15 A.
A quick check
For 100 Ω and 200 Ω across 12 V: series resistance is 300 Ω and current 0.04 A. Parallel resistance is about 66.67 Ω and total current 0.18 A.
Inside the default experiment
- R = 100 + 200 = 300 Ω.
- Total current = 12/300 = 0.04 A.
- Voltage drops: V₁ = 4 V; V₂ = 8 V.
When this model applies
Two ideal ohmic resistors, ideal DC source, zero-resistance wires.
Make a prediction. Then test it.
Switch from series to parallel without changing the resistors. Compare total current.
Try it: Resistors in series & parallel simulation ↗Frequently asked questions
Wondering about the why? Start here.
Why is parallel resistance smaller?
Parallel branches offer additional paths for current. At the same voltage, the total current rises, so equivalent resistance V/I falls.
Do series resistors each get the full voltage?
No. They share the supply voltage in proportion to their resistances. Their voltage drops add up to the supply.