Resistors in series & parallel simulation
Switch two resistors between series and parallel to compare their equivalent resistance, current and voltage drops. In series the resistances add, R = R₁ + R₂, and the same current flows through both. In parallel the reciprocals add, 1/R = 1/R₁ + 1/R₂ (for two resistors, R = R₁R₂ / (R₁ + R₂)), and each branch has the full supply voltage.
What if you changed…
Switch from series to parallel without changing the resistors. Compare total current.
See the calculation
- R = 100 + 200 = 300 Ω.
- Total current = 12/300 = 0.04 A.
- Voltage drops: V₁ = 4 V; V₂ = 8 V.
What this model assumes
Two ideal ohmic resistors, ideal DC source, zero-resistance wires.
Keep an eye on this
Current is shared equally between parallel branches only when their resistances are equal.
Understand the physics ↗Formulas used in this simulation
- 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
Series & parallel resistors: common questions
Wondering about the why? Start here.
What is the formula for resistors in series and parallel?
Series: add the resistances, R = R₁ + R₂ + …. Parallel: add the reciprocals, 1/R = 1/R₁ + 1/R₂ + …. For exactly two parallel resistors, R = R₁R₂ / (R₁ + R₂).
Is the current the same in series or in parallel?
Current is the same through components in series. Voltage is the same across parallel branches, and the branch currents add up to the total current.
How can I check my circuit answer?
In series, the voltage drops must add up to the supply voltage. In parallel, the branch currents must add up to the total current. The simulation shows both checks in its calculation steps.
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.