benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 8858 / If R is the total resistance of three resistors, connected in parallel, with…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

If RR is the total resistance of three resistors, connected in parallel, with resistances R1,R2,R3R_1, R_2, R_3, then 1R=1R1+1R2+1R3 \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} If the resistances are measured in ohms as R1=25ΩR_1=25 \Omega, R2=40ΩR_2=40 \Omega, and R3=50ΩR_3=50 \Omega, with a possible error of 0.5%0.5 \% in each case, estimate the maximum error in the calculated value of RR.
Plain-text mathematical notation (without MathML)
 If R is the total resistance of three resistors, connected in parallel, with resistances R₁,R₂,R₃, then
(1)/(R)=(1)/(R₁)+(1)/(R₂)+(1)/(R₃)
If the resistances are measured in ohms as R₁=25Ω, R₂=40Ω, and R₃=50Ω, with a possible error of 0.5% in each case, estimate the maximum error in the calculated value of R.
Original LaTeX notation
 If $R$ is the total resistance of three resistors, connected in parallel, with resistances $R_1, R_2, R_3$, then
$$
\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}
$$
If the resistances are measured in ohms as $R_1=25 \Omega$, $R_2=40 \Omega$, and $R_3=50 \Omega$, with a possible error of $0.5 \%$ in each case, estimate the maximum error in the calculated value of $R$.

category

math

options

  1. $\frac{1}{20}$ $\Omega$
  2. $\frac{1}{10}$ $\Omega$
  3. $\frac{1}{14}$ $\Omega$
  4. $\frac{1}{25}$ $\Omega$
  5. $\frac{1}{15}$ $\Omega$
  6. $\frac{1}{12}$ $\Omega$
  7. $\frac{1}{22}$ $\Omega$
  8. $\frac{1}{17}$ $\Omega$
  9. $\frac{1}{30}$ $\Omega$
  10. $\frac{1}{18}$ $\Omega$

src

scibench-calculus

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
8858
task_id
8a235e1b-50c6-5ffa-b824-fe8b62d64fd0
task_key
default--test--8858
task_revision_id
1
config / split
default / test

Official source

initial import