Question

Cho các điện trở: R₁= 1Ω, R₂=\(\dfrac{1}{2}\)Ω, R₃=\(\dfrac{1}{3}\) Ω,...., R₂₀₂₁= \(\dfrac{1}{2021}\)Ω mắc song song với nhau. Tính điện trở tương đương của đoạn mạch

Answer 1

\(\Rightarrow\dfrac{1}{Rtd}=\dfrac{1}{R1}+\dfrac{1}{R2}+....+\dfrac{1}{R2021}\)

\(\Rightarrow\dfrac{1}{Rtd}=\dfrac{1}{1}+\dfrac{1}{\dfrac{1}{2}}+\dfrac{1}{\dfrac{1}{3}}+....+\dfrac{1}{\dfrac{1}{2021}}\)

\(\Rightarrow\dfrac{1}{Rtd}=1+2+3+....+2021\)

 \(A=1+2+3+....+2021\)

\(A=2021+2020+2019+...+1\)

\(\Rightarrow2A=2022+2022+...+2022\)(co 2021 so 2022)

\(\Rightarrow2A=2022.2021\Rightarrow A=\dfrac{2022.2021}{2}=2043231\)

\(\Rightarrow\dfrac{1}{Rtd}=A\Rightarrow Rtd=4,89.10^{-7}\left(\Omega\right)\)