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Two Resistors in Parallel

Also known as parallel resistance · product over sum

Rt=R1R2R1+R2R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

Worked example: 4 Ω ∥ 12 Ω → 3 Ω — press Try an example to run it live, then adjust anything.

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Two Resistors in Parallel explained

R1R2Rt

Wired side by side, two resistors give the current two paths at once, so more current flows for the same voltage and the combination resists less than either branch alone. The tidy product-over-sum form is just 1/Rt = 1/R1 + 1/R2 rearranged — conductances, not resistances, are what add in parallel. Worked example: 100 Ω in parallel with 25 Ω gives (100 × 25)/(100 + 25) = 2500/125 = 20 Ω, comfortably below the smaller branch.

Two handy special cases: equal resistors in parallel halve (two 100 Ω resistors make 50 Ω), and a much smaller resistor dominates — 10 Ω in parallel with 10 kΩ is essentially 10 Ω. Household outlets are wired in parallel so every appliance sees full mains voltage. When solving for a branch, the other resistance must exceed the total, since the total is always the smallest value in the circuit.

Two Resistors in Parallel formula

Rt=R1R2R1+R2R_{t} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}
Where
  • RtR_{t}= Total resistance (Ω)
  • R1R_{1}= Resistance 1 (Ω)
  • R2R_{2}= Resistance 2 (Ω)

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Part of this formula set

Series and parallel networks

4 formulasCombining resistors and capacitors two at a time — and the reason the two components follow exactly opposite rules.