شاه کلید نکات
شاه کلید سوال
شکل زیر پنج مقاومت 8 اهمی را نشان می دهد.
الف مقاومت معادل بین نقطه های F و H چقدر است؟
ب مقاومت معادل بین نقطه های F و G چقدر است؟
الف
\(\begin{array}{l}{R_{12}} = {R_1} + {R_2} = 8 + 8 = 16{\mkern 1mu} \Omega \\\\{R_{45}} = {R_4} + {R_5} = 8 + 8 = 16{\mkern 1mu} \Omega \\\\\frac{1}{{{R_{HF}}}} = \frac{1}{{{R_{12}}}} + \frac{1}{{{R_{45}}}} + \frac{1}{{{R_3}}} = \frac{1}{{16}} + \frac{1}{{16}} + \frac{1}{8} = \frac{{1 + 1 + 2}}{{16}} = \frac{4}{{16}} = \frac{1}{4}\\\\ \to {R_{HF}} = 4{\mkern 1mu} \Omega \end{array}\)
ب
\(\begin{array}{l}{R_{1,2}} = {R_1} + {R_2} = 8 + 8 = 16{\mkern 1mu} \Omega \\\\\frac{1}{{{R_{3,12}}}} = \frac{1}{{{R_3}}} + \frac{1}{{{R_{12}}}} = \frac{1}{8} + \frac{1}{{16}} = \frac{{2 + 1}}{{16}} = \frac{3}{{16}} \to {R_{3,12}} = \frac{{16}}{3}{\mkern 1mu} \Omega \\\\{R_{5,312}} = {R_{3,12}} + {R_5} = \frac{{16}}{3} + 8 = \frac{{16 + 24}}{3} = \frac{{40}}{3}{\mkern 1mu} \Omega \\\\\frac{1}{{{R_{FG}}}} = \frac{1}{{{R_4}}} + \frac{1}{{{R_{5,312}}}} = \frac{1}{8} + \frac{3}{{40}} = \frac{{5 + 3}}{{40}} = \frac{8}{{40}} = \frac{1}{5}\\\\ \to {R_{FG}} = 5{\mkern 1mu} \Omega \end{array}\)
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