Đáp án:
B
Giải thích các bước giải:
Ta có: \(x + y = 16\)
Áp dụng phương pháp nguồn điện tương đương:
\(\begin{array}{l}
\dfrac{1}{{{r_b}}} = \dfrac{1}{{{r_1}}} + \dfrac{1}{{{r_2}}} + \dfrac{1}{R} = \dfrac{1}{{0,4x}} + \dfrac{1}{{0,4y}} + \dfrac{1}{6}\\
\Rightarrow \dfrac{1}{{{r_b}}} = \dfrac{{x + y}}{{0,4xy}} + \dfrac{1}{6} = \dfrac{{16}}{{0,4xy}} + \dfrac{1}{6}\\
\Rightarrow \dfrac{1}{{{r_b}}} = \dfrac{{40}}{{xy}} + \dfrac{1}{6} = \dfrac{{240 + xy}}{{6xy}}\\
{U_{AB}} = \dfrac{{\dfrac{{{e_1}}}{{{r_1}}} + \dfrac{{{e_2}}}{{{r_2}}} + \dfrac{{{e_3}}}{R}}}{{\dfrac{1}{{{r_b}}}}} = \dfrac{{\dfrac{{1,8x}}{{0,4x}} + \dfrac{{1,8y}}{{0,4y}} + \dfrac{0}{6}}}{{\dfrac{{240 + xy}}{{6xy}}}}\\
\Rightarrow {U_{AB}} = \dfrac{9}{{\dfrac{{240 + xy}}{{6xy}}}} = \dfrac{{54xy}}{{240 + xy}}\\
{I_2} = \dfrac{{{e_2} - {U_{AB}}}}{{{r_2}}} = \dfrac{{1,8y - \dfrac{{54xy}}{{240 + xy}}}}{{0,4y}} = 4,5 - \dfrac{{135x}}{{240 + xy}}\\
\Rightarrow 4,5 - \dfrac{{135x}}{{240 + xy}} = 0 \Rightarrow 240 + xy = 30x\\
\Rightarrow 240 + x\left( {16 - x} \right) = 30x\\
\Rightarrow x = 10\\
\Rightarrow y = 6
\end{array}\)
