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Question Number 191626 by yaba1 last updated on 27/Apr/23

Answered by a.lgnaoui last updated on 28/Apr/23

$$\mathrm{Calcul}\mathrm{de}\mathrm{Resistance}\mathrm{dans}\mathrm{les}4\mathrm{circuits}$$$$\bullet 1\mathbf{a}\mathbf{U}=\mathbf{RI}\mathrm{avec}\frac{1}{\mathrm{R}}=\frac{1}{\mathrm{R}1}+\frac{1}{\mathrm{R}2}+\frac{1}{\mathrm{R}3}$$$$=\frac{\mathrm{R}1+\mathrm{R}2}{\mathrm{R}1\times \mathrm{R}2}+\frac{1}{\mathrm{R}3}=\frac{(\mathrm{R}1\times \mathrm{R}3+\mathrm{R}2\times \mathrm{R}3+\mathrm{R}1\times \mathrm{R}2)}{\mathrm{R}1\times \mathrm{R}2\times \mathrm{R}3}$$$$\mathbf{R}=\frac{\mathrm{R}1\times \mathrm{R}2\times \mathrm{R}3}{\mathrm{R}1\times \mathrm{R}2+\mathrm{R}2\times \mathrm{R}3+\mathrm{R}1\times \mathrm{R}3}$$$$$$$$\mathrm{R}=\frac{7\times 5\times 2}{\left(7\times 5\right)+\left(5\times 2\right)+\left(7\times 2\right)}=\frac{70}{35+10+14}$$$$$$$$\mathbf{R}=\frac{70}{59}=1,18\mathbf{\Omega }$$$$\bullet 1\mathbf{b}\mathbf{R}=\mathbf{R}1+\mathbf{R}2=2+5$$$$\mathbf{R}=7\mathbf{\Omega }$$$$\bullet 1\mathbf{c}\mathbf{R}=\mathbf{R}1+\mathbf{R}2+\mathbf{R}3=2+5+7$$$$\mathbf{R}=14$$$$\bullet 2\mathbf{R}=\mathbf{R}1+{\mathbf{R}}_{\mathbf{eq}}$$$$\frac{1}{{\mathbf{R}}_{\mathbf{eq}}}=\frac{1}{(\mathbf{R}2+\mathbf{R}3)}+\frac{1}{(\mathbf{R}6+\frac{\mathbf{R}4\times \mathbf{R}5}{\mathbf{R}4+\mathbf{R}5})}$$$$=\frac{1}{\mathbf{R}2+\mathbf{R}3}+\frac{\mathbf{R}4+\mathbf{R}5}{\mathbf{R}6(\mathbf{R}4+\mathbf{R}5)+\left(\mathbf{R}4\times \mathbf{R}5\right)}$$$$=\frac{\mathbf{R}6(\mathbf{R}4+\mathbf{R}5)+\left(\mathbf{R}4\times \mathbf{R}5\right)+(\mathbf{R}4+\mathbf{R}5)(\mathbf{R}2+\mathbf{R}3)}{(\mathbf{R}2+\mathbf{R}3)[\mathbf{R}6(\mathbf{R}4+\mathbf{R}5)+\mathbf{R}4\times \mathbf{R}5]}$$$$$$$$=\frac{(\mathbf{R}4+\mathbf{R}5)(\mathbf{R}2+\mathbf{R}3+\mathbf{R}6)+\left(\mathbf{R}4\times \mathbf{R}5\right)}{(\mathbf{R}2+\mathbf{R}3)[\mathbf{R}6(\mathbf{R}4+\mathbf{R}5)+\mathbf{R}4\times \mathbf{R}5]}$$$$$$$$\mathbf{Req}=\frac{(\mathbf{R}2+\mathbf{R}3)[\mathbf{R}6(\mathbf{R}4+\mathbf{R}5)+\mathbf{R}4\times \mathbf{R}5]}{(\mathbf{R}4+\mathbf{R}5)(\mathbf{R}2+\mathbf{R}3+\mathbf{R}6)+\left(\mathbf{R}4\times \mathbf{R}5\right)}$$$$$$$$\mathbf{R}=\mathbf{R}1+{\mathbf{R}}_{\mathbf{eq}}$$$$$$$$\mathbf{R}=80+\frac{(49+51)[75(37+45)+\left(37\times 45\right)]}{(37+45)(49+51+75)+\left(37\times 45\right)}$$$$$$$$=80+\frac{100[75\times 82+37\times 45]}{82\times 175+37\times 45}=128,798$$$$$$$$\mathbf{R}=128,798\mathbf{\Omega }$$

Answered by a.lgnaoui last updated on 28/Apr/23

$$\mathrm{Calcul}\mathrm{de}\mathrm{Capacite}\mathrm{equivalante}$$$$\bullet {\mathbf{a}}_{12}\mathbf{capacites}\mathbf{en}\mathbf{paralele}$$$$\mathrm{I}=\mathrm{I}1+\mathrm{I}2\Rightarrow \mathbf{U}=\mathbf{U}$$$$\Rightarrow \mathbf{C}=\mathbf{C}1+\mathbf{C}2+\mathbf{C}3=12+20+30$$$$$$$$]\mathbf{C}=62\mathit{\eta }\mathbf{F}$$$$$$$${\mathbf{b}}_{12}\mathbf{capacites}\mathbf{en}\mathbf{serie}$$$$\frac{1}{\mathbf{C}}=\frac{1}{\mathbf{C}1}+\frac{1}{\mathbf{C}2}+\frac{1}{\mathbf{C}3}=\frac{\mathbf{C}1+\mathbf{C}2}{\mathbf{C}1.\mathbf{C}2}+\frac{1}{\mathbf{C}3}$$$$=\frac{\mathbf{C}3(\mathbf{C}1+\mathbf{C}2)+\mathbf{C}1.\mathbf{C}2}{\mathbf{C}1.\mathbf{C}2.\mathbf{C}3}$$$$\Rightarrow \mathbf{C}=\frac{\mathbf{C}1.\mathbf{C}2.\mathbf{C}3}{\mathbf{C}3(\mathbf{C}1+\mathbf{C}2)+\mathbf{C}1.\mathbf{C}2}$$$$\mathbf{C}=\frac{17\times 20\times 30}{30(17+20)+17\times 20}=\frac{1020}{145}$$$$$$$$\mathbf{C}=7,034\mathit{\eta }\mathbf{F}$$

Answered by manxsol last updated on 28/Apr/23

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