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04 Electricity and Signals

Total Resistance of Two Resistors in Parallel

Card No. 04·0023 · Updated · Standard formula, shown below

Total resistance 68.75 Ω
Total current
0.1745 A
Result
Current through R1
0.1200 A
Result
Current through R2
0.0545 A
Result
You enter
Resistor R1, Resistor R2, Voltage across them
You get
Total resistance, Total current, Current through R1, Current through R2
Rounding
2 dp · 4 dp

This calculator finds the total (equivalent) resistance of two resistors connected in parallel. Enter both resistances and the voltage across them; you get the total resistance, the total current and the current in each branch.

Formula

For resistors in parallel the conductances add: 1 ÷ Rt = 1 ÷ R1 + 1 ÷ R2, so Rt = R1 × R2 ÷ (R1 + R2) for two resistors. Each branch has the full voltage across it, so by Ohm’s law I1 = V ÷ R1, I2 = V ÷ R2 and the total current is V ÷ Rt = I1 + I2.

  • R1, R2: resistances in ohms
  • V: voltage across the pair, volts

Worked Example

R1 = 100 Ω, R2 = 220 Ω, 12 V.

  1. Rt = 100 × 220 ÷ (100 + 220) = 22,000 ÷ 320 = 68.75 Ω
  2. Total current = 12 ÷ 68.75 = 0.1745 A
  3. I1 = 12 ÷ 100 = 0.1200 A; I2 = 12 ÷ 220 = 0.0545 A
  4. Check: 0.1200 + 0.0545 = 0.1745 A

Limits and common mistakes

  • The total is always smaller than the smallest resistor.
  • Two equal resistors in parallel give half of one.
  • This is pure resistance. For AC impedance with capacitors or inductors, the reactances add as complex numbers, not like this.
  • Check resistor power: P = V² ÷ R (1.44 W in R1 here).
Formula used
in r1 | Resistor R1 | Ω | 100 | 0
in r2 | Resistor R2 | Ω | 220 | 0
in v | Voltage across them | V | 12 | 0
out rt | Total resistance | Ω | 1 / (1 / r1 + 1 / r2) | 2
out it | Total current | A | v / rt | 4
out i1 | Current through R1 | A | v / r1 | 4
out i2 | Current through R2 | A | v / r2 | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: colour-banded resistors soldered side by side on a green circuit board.
Save this card: a 1000 × 1500 image of Total Resistance of Two Resistors in Parallel.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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