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What is the total resistance of 10-, 20-, and 50-ohm resistors connected in parallel?

About 5.9 ohms, lower than the smallest resistor.

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  1. 5.9 ohms ✔
  2. 17 ohms
  3. 80 ohms

Why: In parallel, add the reciprocals: 1/10 + 1/20 + 1/50 is 0.17, so the total is about 5.9 ohms. Parallel resistance is always lower than the smallest branch.

Huh, didn't know that: Connected in series, the same three resistors would add up to 80 ohms.

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Why did Mr. Ohm marry Mrs. Ohm? Because he couldn't resistor!
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References

Answer: 5.9 ohms. In parallel, add the reciprocals: 1/10 + 1/20 + 1/50 is 0.17, so the total is about 5.9 ohms. Parallel resistance is always lower than the smallest branch.

  1. NCVEC 2023-2027 General Class Pool and Syllabus (6th Errata, Feb 4 2026) ncvec.org/downloads/General%20Class%20Pool%20and%20Syllabus%202023-2027%20Public%20Release%20with%206th%20Errata%20Feb%204%202026.pdf
    5.9 ohms
    Checked 2026-10-11.
  2. Resistors in Series and Parallel (OpenStax University Physics via LibreTexts) phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/10%3A_Direct-Current_Circuits/10.03%3A_Resistors_in_Series_and_Parallel
    less than the smallest of the individual resistances
    Checked 2026-10-11.

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