Đáp án:
${R_1} = 8\sqrt 2 \Omega = 11,3\Omega $
Giải thích các bước giải:
Ta có:
$\begin{array}{l}
{R_d} = \dfrac{{{U_d}}}{{{I_d}}} = \dfrac{6}{{0,75}} = 8\Omega \\
{I_1} = \dfrac{{{U_d}}}{{{R_1}}} = \dfrac{6}{{{R_1}}}\\
I = {I_d} + {I_1} = 0,75 + \dfrac{6}{{{R_1}}} = \dfrac{{3{R_1} + 24}}{{4{R_1}}} = \dfrac{{3\left( {{R_1} + 8} \right)}}{{4{R_1}}}\\
{R_{td}} = \dfrac{{{U_{MN}}}}{I}\\
\Leftrightarrow {R_b} - {R_1} + \dfrac{{{R_1}{R_d}}}{{{R_1} + {R_d}}} = \dfrac{{{U_{MN}}}}{I}\\
\Leftrightarrow 16 - {R_1} + \dfrac{{8{R_1}}}{{{R_1} + 8}} = \dfrac{{16{R_1}}}{{{R_1} + 8}}\\
\Leftrightarrow 16 - {R_1} = \dfrac{{8{R_1}}}{{{R_1} + 8}}\\
\Leftrightarrow {R_1}^2 - 8{R_1} + 128 = - 8{R_1}\\
\Leftrightarrow {R_1} = 8\sqrt 2 = 11,3\Omega
\end{array}$
