Library / Electrical / ELE-25
Electrical
Three resistors in parallel
Combined resistance is always smaller than the smallest branch, because each added path gives the current another way through.
- Ref
- ELE-25
- Rev
- v1
- Field
- Electrical
- Result
- R [Ω]
R₁, R₂ and R₃ are three resistors connected across the same two points, so each has the same voltage. Their conductances (1/R) add. The combined resistance is always lower than the smallest branch, since each branch gives the current another path.
Combined resistance is always smaller than the smallest branch, because each added path gives the current another way through.
Calculator
- Total conductance 1/R18.33 mS
- Share of the current taken by R₁54.55 %
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The default result of 54.5 Ω is lower than the smallest resistor (100 Ω): adding a branch can only lower the resistance.
- The smallest resistor takes the largest share of the current and dominates the answer. A tiny resistance in parallel with a large one effectively shorts it out.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Ω) | Local step | Change in result |
|---|---|---|---|---|---|---|
| R1 First resistor | 1 to 100,000 Ω | 0.9917 | 119.9 | 118.9 | +10% | +5.22 % |
| R2 Second resistor | 1 to 100,000 Ω | 0.9868 | 74.94 | 73.96 | +10% | +2.54 % |
| R3 Third resistor | 1 to 100,000 Ω | 0.9852 | 66.62 | 65.64 | +10% | +1.68 % |
Sweep of First resistor
| First resistor (Ω) | Combined resistance (Ω) |
|---|---|
| 1 | 0.9917 |
| 4.217 | 4.074 |
| 17.78 | 15.49 |
| 74.99 | 46.15 |
| 316.2 | 86.99 |
| 1,334 | 110.1 |
| 5,623 | 117.5 |
| 23,710 | 119.4 |
| 100,000 | 119.9 |
Sweep one variable
Variables and how each one contributes
Combined resistance
What the equation gives you. Everything else feeds it.
First resistor
The first resistor. The largest effect at the default, because it carries the most current: a 10 % rise in R₁ raises R by about 5 %.
Second resistor
The second resistor. Moderate effect: a 10 % rise in R₂ raises R by about 2.5 %.
Third resistor
The third resistor. Smallest effect at the default, because it carries the least current: a 10 % rise in R₃ raises R by about 1.7 %.
Worked example with the values above
- Reciprocals: 1/100 = 0.01, 1/200 = 0.005, 1/300 = 0.003333 S.
- Sum: 0.018333 S.
- R = 1 / 0.018333 = 54.55 Ω.
Assumptions and limits
- All three resistors share the same two terminals and so the same voltage.
- Ideal resistors, with no heating or lead resistance.
Common mistakes
- Adding the resistances as for a series circuit.
- Forgetting to invert the sum of reciprocals at the end.
Statistics and uncertainty
The relative effect of each resistor equals the share of the current it carries (here 55 %, 27 % and 18 %). A 5 % tolerance on each resistor gives roughly a 3 % tolerance on the combination, because the independent errors partly average out.
Where it is used
- Combining parallel loads or redundant paths into one equivalent.
- Choosing a low resistance by joining several larger ones.
Maths you need
- Reciprocals: 1/R
- Ohm’s law: V = IR