Bonsoir svp c des maths niveau 4 eme Mrc d avances.... Pergunta de ideia deLinocha03

May 2019 1 24 Report

Bonsoir svp c des maths niveau 4 eme Mrc d avances.

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Commentaires (3) Bonjour Linocha03

$\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\\\\\\1)\ a)\ \dfrac{1}{R}=\dfrac{1}{2}+\dfrac{1}{5}\\\\\dfrac{1}{R}=\dfrac{5}{10}+\dfrac{2}{10}\\\\\dfrac{1}{R}=\dfrac{7}{10}\\\\\\\Longrightarrow\boxed{R=\dfrac{10}{7}\ \Omega\approx1,4\ \Omega}\\\\\\\\b)\ \dfrac{1}{R}=\dfrac{1}{4}+\dfrac{1}{13}\\\\\dfrac{1}{R}=\dfrac{13}{52}+\dfrac{4}{42}\\\\\dfrac{1}{R}=\dfrac{17}{52}\\\\\\\Longrightarrow\boxed{R=\dfrac{52}{17}\ \Omega\approx3\ \Omega}$

$c)\ \dfrac{1}{R}=\dfrac{1}{11}+\dfrac{1}{13}\\\\\dfrac{1}{R}=\dfrac{13}{143}+\dfrac{11}{143}\\\\\dfrac{1}{R}=\dfrac{24}{143}\\\\\\\Longrightarrow\boxed{R=\dfrac{143}{24}\ \Omega\approx6\ \Omega}$

Exercice 2

$\dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}\Longrightarrow\boxed{\dfrac{1}{R_1}=\dfrac{1}{R}-\dfrac{1}{R_2}}\\\\\\a)\dfrac{1}{R_1}=\dfrac{1}{6}-\dfrac{1}{24}\\\\\dfrac{1}{R_1}=\dfrac{4}{24}-\dfrac{1}{24}\\\\\dfrac{1}{R_1}=\dfrac{3}{24}\\\\R_1=\dfrac{24}{3}\\\\\Longrighrattow\boxed{R_1=8\ \Omega}$

$b)\ \dfrac{1}{R_1}=\dfrac{1}{1,1}-\dfrac{1}{1,7}\\\\\dfrac{1}{R_1}=\dfrac{10}{11}-\dfrac{10}{17}\\\\\dfrac{1}{R_1}=\dfrac{170}{187}-\dfrac{110}{187}\\\\\dfrac{1}{R_1}=\dfrac{60}{187}\\\\R_1=\dfrac{187}{60}\\\\\Longrighrattow\boxed{R_1\approx3,1\ \Omega}$

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