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Question Number 146100 by tabata last updated on 10/Jul/21

Commented by tabata last updated on 10/Jul/21

$$inthefollowingfigure,calculatetheequivalentresistanceofthe$$$$externalcircuitandthencalculatethecurrentthroughit?$$

Answered by Olaf_Thorendsen last updated on 10/Jul/21

$${\mathrm{R}}_{\mathrm{ab}}=2\mathrm{\Omega }\Rightarrow \frac{1}{{\mathrm{R}}_{\mathrm{ab}}}=\frac{1}{2}{\mathrm{\Omega }}^{-1}$$$$\frac{1}{{\mathrm{R}}_{\mathrm{cd}}}=\frac{1}{5}+\frac{1}{8}+\frac{1}{12}=\frac{49}{120}{\mathrm{\Omega }}^{-1}$$$${\mathrm{R}}_{\mathrm{ef}}=\frac{1}{\frac{1}{7}+\frac{1}{6}}+3=\frac{81}{13}\mathrm{\Omega }\Rightarrow \frac{1}{{\mathrm{R}}_{\mathrm{ef}}}=\frac{13}{81}{\mathrm{\Omega }}^{-1}$$$$\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{1}{{\mathrm{R}}_{\mathrm{ab}}}+\frac{1}{{\mathrm{R}}_{\mathrm{cd}}}+\frac{1}{{\mathrm{R}}_{\mathrm{ef}}}=\frac{1}{2}+\frac{49}{120}+\frac{13}{81}$$$$\frac{1}{{\mathrm{R}}_{\mathrm{eq}}}=\frac{3463}{3240}\Rightarrow {\mathrm{R}}_{\mathrm{eq}}=\frac{3240}{3463}\approx 0,94\mathrm{\Omega }$$$${\mathrm{U}}_{\mathrm{eq}}={\mathrm{U}}_{\mathrm{ab}}={\mathrm{U}}_{\mathrm{cd}}={\mathrm{U}}_{\mathrm{ef}}=20\mathrm{V}$$$${\mathrm{I}}_{\mathrm{eq}}=\frac{{\mathrm{U}}_{\mathrm{eq}}}{{\mathrm{R}}_{\mathrm{eq}}}=20\times \frac{3463}{3240}=\frac{3463}{162}\approx 21,38\mathrm{A}$$

Commented by tabata last updated on 10/Jul/21

$$sir{R}_{cd}=\frac{1}{5}+\frac{1}{8}+\frac{1}{1.2}not\frac{1}{5}+\frac{1}{8}+\frac{1}{12}$$

Commented by tabata last updated on 11/Jul/21

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