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Resistors in parallel
Beginner
Reciprocals add.
1/R = 1/R₁+1/R₂Each gets the full voltage, currents add and 1/R = 1/R₁ + 1/R₂. The total is smaller than the smallest branch.
10 Ω ∥ 10 Ω = 5 Ω.
Adding a branch always reduces the total resistance.
In more detail
In parallel, resistors share the same voltage, and the reciprocal of the total resistance is the sum of the reciprocals, 1/R = 1/R1 + 1/R2 + ... The total is smaller than any individual resistor.
Real-world uses
- Household appliances are wired in parallel so each receives full voltage.
- Parallel resistors are used to share current in high-power circuits.
- Car headlights are wired in parallel, so each bulb gets the full battery voltage and keeps working if the other fails.
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Frequently asked questions
Why does parallel reduce resistance?
Because current has more paths to flow through, so the overall resistance drops.
Does a failure stop the others?
No. Each branch works independently in a parallel circuit.
Why is the total resistance smaller in parallel?
Each extra branch gives the current another path, so the combined resistance is less than the smallest branch.
Related topics in Current Electricity & Circuits
Superconductors · Semiconductors and thermistors · Resistors in series · Colour code of resistors · Electric power · Heating effect of current