Question Number 143751 by help last updated on 17/Jun/21
Answered by TheHoneyCat last updated on 17/Jun/21
$$\mathrm{let}\:{R}_{\mathrm{0}} ={r} \\ $$$$\mathrm{I}\:\mathrm{will}\:\mathrm{right}\:{R}_{{ijk}} \:\mathrm{for}\:\mathrm{the}\:\mathrm{total}\:\mathrm{resistance}\:\mathrm{of}\:{i},{j}\:\mathrm{and}\:{k}... \\ $$$$ \\ $$$${R}_{\mathrm{34}} =\frac{{R}_{\mathrm{3}} {R}_{\mathrm{4}} }{{R}_{\mathrm{3}} +{R}_{\mathrm{4}} } \\ $$$${R}_{\mathrm{234}} ={R}_{\mathrm{2}} +{R}_{\mathrm{34}} \\ $$$${R}_{\mathrm{1234}} =\frac{{R}_{\mathrm{1}} {R}_{\mathrm{234}} }{{R}_{\mathrm{1}} +{R}_{\mathrm{234}} }=\frac{{R}_{\mathrm{1}} \left({R}_{\mathrm{2}} +{R}_{\mathrm{34}} \right)}{{R}_{\mathrm{1}} +{R}_{\mathrm{2}} +{R}_{\mathrm{34}} }=\frac{{R}_{\mathrm{1}} \left({R}_{\mathrm{2}} +\frac{{R}_{\mathrm{3}} {R}_{\mathrm{4}} }{{R}_{\mathrm{3}} +{R}_{\mathrm{4}} }\right)}{{R}_{\mathrm{1}} +{R}_{\mathrm{2}} +\frac{{R}_{\mathrm{3}} {R}_{\mathrm{4}} }{{R}_{\mathrm{3}} +{R}_{\mathrm{4}} }} \\ $$$${R}_{\mathrm{012345}} ={R}_{\mathrm{0}} +{R}_{\mathrm{5}} +\frac{{R}_{\mathrm{1}} {R}_{\mathrm{2}} \left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)+{R}_{\mathrm{1}} {R}_{\mathrm{3}} {R}_{\mathrm{4}} }{\left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)\left({R}_{\mathrm{1}} +{R}_{\mathrm{2}} \right)+{R}_{\mathrm{3}} {R}_{\mathrm{4}} } \\ $$$${R}_{\mathrm{012345}} =\frac{\left({R}_{\mathrm{0}} +{R}_{\mathrm{5}} \right)\left(\left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)\left({R}_{\mathrm{1}} +{R}_{\mathrm{2}} \right)+{R}_{\mathrm{3}} {R}_{\mathrm{4}} \right)+{R}_{\mathrm{1}} {R}_{\mathrm{2}} \left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)+{R}_{\mathrm{1}} {R}_{\mathrm{3}} {R}_{\mathrm{4}} }{\left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)\left({R}_{\mathrm{1}} +{R}_{\mathrm{2}} \right)+{R}_{\mathrm{3}} {R}_{\mathrm{4}} } \\ $$$$ \\ $$$$\mathrm{and}\:{I}=\frac{\delta}{{R}_{\mathrm{012345}} }=\frac{\delta\left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)\left({R}_{\mathrm{1}} +{R}_{\mathrm{2}} \right)+\delta{R}_{\mathrm{3}} {R}_{\mathrm{5}} }{\left({r}+{R}_{\mathrm{5}} \right)\left(\left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)\left({R}_{\mathrm{1}} +{R}_{\mathrm{2}} \right)+{R}_{\mathrm{3}} {R}_{\mathrm{4}} \right)+{R}_{\mathrm{1}} {R}_{\mathrm{2}} \left({R}_{\mathrm{3}} +{R}_{\mathrm{4}} \right)+{R}_{\mathrm{1}} {R}_{\mathrm{3}} {R}_{\mathrm{4}} } \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{do}\:\mathrm{forgive}\:\mathrm{me}\:\mathrm{for}\:\mathrm{not}\:\mathrm{computing}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{too}\:\mathrm{tired}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{on}. \\ $$$$ \\ $$$$\Bumpeq\bullet\left(\right. \\ $$
Commented by Ar Brandon last updated on 18/Jun/21
Vous êtes merveilleux. Heureux de vous avoir parmi nous, monsieur��
Commented by Dwaipayan Shikari last updated on 18/Jun/21
$$ \: \: \: \: \: \: \: \\ $$
Commented by Ar Brandon last updated on 18/Jun/21
Je vous ai longtemps observé et vos différentes solutions aux exercices envoyés dans ce forum. Bravo !
Commented by TheHoneyCat last updated on 18/Jun/21
Merci, que de compliments. Mais il n'y a rien qui le mérite sur cette question. J'avais juste beaucoup trop de temps à perdre.��
Commented by TheHoneyCat last updated on 18/Jun/21
Non, je suis en prépa MP, et je ne voulais juste pas aller me coucher. �� Si j'avais été un vrai physicien, j'aurais précisé que r<<R5 ce qui aurait un peu simplifié le calcul. Et surtout, je n'aurai pas oublié de faire l'application numérique.
Commented by ArielVyny last updated on 18/Jun/21
vous êtes physicien?
Commented by Dwaipayan Shikari last updated on 18/Jun/21
$${Translate}\:!!\: \\ $$
Commented by TheHoneyCat last updated on 18/Jun/21
$$ \\ $$$${Well},\:{since}\:{it}\:{is}\:{asked}\:{so}\:{nicely}. \\ $$$${I}\:{was}\:{very}\:{nicely}\:{complimented}. \\ $$$${I}\:{answered}\:{it}\:{was}'{nt}\:{much} \\ $$$${I}\:{was}\:{then}\:{asked}\:{if}\:{I}\:{happed}\:{to}\:{be}\:{a}\:{physicist}. \\ $$$${I}\:{said}\:{I}\:{was}'{nt}. \\ $$$${I}\:{also}\:{made}\:{the}\:{folowing}\:{joke}: \\ $$$${One}\:{could}\:{have}\:{guessed}\:{it}, \\ $$$${for}\:{I}\:{forgot}\:{to}\:{mention}\:{that}\:{r}\ll{R}_{\mathrm{5}} \\ $$$${and}\:{also}\:{forgot}\:{to}\:{give}\:{the}\:{numerical}\:{result} \\ $$$${two}\:{unforgivable}\:{miktakes}\:{a}\:{real}\:{physicist}\:{would}\:{not}\:{do}. \\ $$$$ \\ $$$${Sorry}\:{this}\:{made}\:{you}\:{panic}, \\ $$$${had}\:{it}\:{been}\:{a}\:{usefull}\:{information}\:{I}\:{would}\:{naturaly}\:{have}\:{translated}\:{it} \\ $$$${but}\:{as}\:{you}\:{can}\:{see},\:{it}'{s}\:{just}\:{chatting}... \\ $$$$\left.;\bullet\right) \\ $$
Commented by Dwaipayan Shikari last updated on 18/Jun/21
$${A}\:{cat}\:{sleeps}\:\mathrm{16}−\mathrm{20}\:{hours}\:{in}\:{a}\:{day}.\:{Thus}\:{that}\:{cat}\: \\ $$$${doesn}'{t}\:{get}\:{time}\:{to}\:{learn}\:{French}.{You}\:{are} \\ $$$${Honey}\:{cat}\:\:{and}\:{i}\:{am}\:{sleepy}\:{cat} \\ $$
Commented by Ar Brandon last updated on 18/Jun/21
Hahaha ! তুমি মজার
Commented by Ar Brandon last updated on 18/Jun/21
😂😂তারা এখনও বুঝতে পারে। তবে এটি আরও কিছু প্রচেষ্টা দাবি করবে।