Đáp án:

a) \(10A\)

b) \(18\Omega \)

c) \(\left[ \begin{array}{l}
{R_4} = \dfrac{{414}}{{47}}\Omega \\
{R_4} = 162\Omega 
\end{array} \right.\)

Giải thích các bước giải:

Mạch gồm: [R1 // R3) nt [R2 // R4)

Ta có: 

\(\begin{array}{l}
{R_{13}} = \dfrac{{{R_1}{R_3}}}{{{R_1} + {R_3}}} = \dfrac{{3.9}}{{3 + 9}} = 2,25\Omega \\
{R_{24}} = \dfrac{{{R_2}{R_4}}}{{{R_2} + {R_4}}} = \dfrac{{6{R_4}}}{{{R_4} + 6}}\\
R = {R_{13}} + {R_{24}} = 2,25 + \dfrac{{6{R_4}}}{{{R_4} + 6}} = \dfrac{{8,25{R_4} + 13,5}}{{{R_4} + 6}}\\
I = \dfrac{U}{R} = \dfrac{{75\left[ {{R_4} + 6} \right)}}{{8,25{R_4} + 13,5}}\\
{I_1} = \dfrac{{{R_3}}}{{{R_1} + {R_3}}}.I = \dfrac{9}{{12}}.\dfrac{{75\left[ {{R_4} + 6} \right)}}{{8,25{R_4} + 13,5}}\\
 \Rightarrow {I_1} = \dfrac{{56,25\left[ {{R_4} + 6} \right)}}{{8,25{R_4} + 13,5}}\\
{I_2} = \dfrac{{{R_4}}}{{{R_2} + {R_4}}}.I = \dfrac{{75{R_4}}}{{8,25{R_4} + 13,5}}\\
{I_{CD}} = \left| {{I_1} - {I_2}} \right| = \left| {\dfrac{{56,25\left[ {{R_4} + 6} \right)}}{{8,25{R_4} + 13,5}} - \dfrac{{75{R_4}}}{{8,25{R_4} + 13,5}}} \right|\\
 \Rightarrow {I_{CD}} = \left| {\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}}} \right|
\end{array}\)

a) Ta có: 

\({I_{CD}} = \left| {\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}}} \right| = \left| {\dfrac{{337,5 - 18,75.2}}{{8,25.2 + 13,5}}} \right| = 10A\)

b) Ta có: 

\(\begin{array}{l}
{I_{CD}} = \left| {\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}}} \right| = 0\\
 \Rightarrow 337,5 - 18,75{R_4} = 0 \Rightarrow {R_4} = 18\Omega 
\end{array}\)

c) Ta có: 

\(\begin{array}{l}
{I_{CD}} = \left| {\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}}} \right| = 2\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}} = 2\\
\dfrac{{337,5 - 18,75{R_4}}}{{8,25{R_4} + 13,5}} =  - 2
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
337,5 - 18,75{R_4} = 2\left[ {8,25{R_4} + 13,5} \right)\\
337,5 - 18,75{R_4} =  - 2\left[ {8,25{R_4} + 13,5} \right)
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
{R_4} = \dfrac{{414}}{{47}}\Omega \\
{R_4} = 162\Omega 
\end{array} \right.
\end{array}\)