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1/Rtotal = 1/R₁ + 1/R₂ + 1/R₃ + ...
For two resistors: Rtotal = (R₁ × R₂) / (R₁ + R₂)
The equivalent resistance of parallel resistors is always less than the smallest individual resistance.
Parallel resistance is the equivalent resistance of two or more resistors connected across the same two nodes, providing multiple paths for current to flow. Unlike series circuits, the total resistance of a parallel combination is always less than the smallest individual resistor because each additional path reduces the overall opposition to current. The voltage across every resistor in a parallel network is identical, while the current divides among the branches inversely proportional to their resistance. This principle is the foundation of current divider circuits, load distribution in power systems, and virtually all practical wiring in buildings and vehicles.
Find all resistors that share the same two connection points. These resistors have identical voltage across them and are in parallel, even if the schematic layout makes them look different.
Compute 1/R1 + 1/R2 + 1/R3 + ... for all resistors. For example, with 100 ohm and 200 ohm: 1/100 + 1/200 = 0.01 + 0.005 = 0.015.
Invert the result: R_total = 1 / 0.015 = 66.67 ohm. For exactly two resistors, you can use the shortcut formula: R_total = (R1 x R2) / (R1 + R2).
The result must be less than the smallest resistor in the combination. If your answer is larger, recheck your arithmetic. A quick test: two equal resistors in parallel give exactly half the value of one.
All outlets in your home are wired in parallel so each device gets the full supply voltage and operates independently. Adding appliances reduces total circuit resistance and increases total current draw.
Parallel resistors divide current among branches, enabling current sharing in power electronics. This is how high-power loads use multiple smaller resistors to handle current no single resistor could manage.
Combining standard resistors in parallel lets engineers create non-standard resistance values with higher precision than any single component, useful in calibration and measurement circuits.
Quick reference for frequently used two-resistor parallel combinations using standard E12 values.
| R1 (Ω) | R2 (Ω) | Parallel Result (Ω) | Use Case |
|---|---|---|---|
| 100 | 100 | 50.0 | Double current capacity |
| 100 | 220 | 68.75 | Approximate 68Ω value |
| 220 | 330 | 132.0 | Non-standard mid-range value |
| 470 | 1,000 | 319.7 | Approximate 330Ω value |
| 1,000 | 1,000 | 500.0 | Precise 500Ω value |
| 1,000 | 4,700 | 824.6 | Approximate 820Ω value |
| 2,200 | 3,300 | 1,320.0 | Non-standard kilohm value |
| 4,700 | 10,000 | 3,197.3 | Approximate 3.3kΩ value |
| 10,000 | 10,000 | 5,000.0 | Precise 5kΩ value |
Each parallel branch provides an additional path for current. Since more paths mean less total opposition, every added resistor reduces the equivalent resistance below that of any single branch. Even adding a very large resistor in parallel will slightly reduce the total.
The remaining branches continue to operate normally because they still have the full supply voltage across them. This is a major advantage of parallel circuits over series circuits, and it is the reason household wiring uses parallel connections.
The shortcut formula R_total = (R1 x R2) / (R1 + R2) only works for exactly two resistors at a time. For three or more, use the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3. Alternatively, combine two at a time using the shortcut and then combine the result with the next resistor.
The total power dissipated by parallel resistors equals the sum of power dissipated by each individual resistor. Since the voltage is the same across each branch, smaller resistors draw more current and dissipate more power. Total power also equals V squared divided by the equivalent resistance.
Placing N identical resistors in parallel gives R/N total resistance and N times the power-handling capacity. This technique is common in power electronics where a single resistor cannot handle the required wattage, or where current sensing requires very low resistance values.