Giải thích các bước giải:
a)
- K mở:
Mạch gồm: \({\rm{[}}({R_1}nt{R_4})\parallel {R_2}{\rm{]nt }}{{\rm{R}}_3}\)
\(\begin{array}{l}
{R_{14}} = {R_1} + {R_4} = 60\\
{R_{AD}} = \dfrac{{{R_{14}}.{R_2}}}{{{R_{14}} + {R_2}}} = 36\\
{R_{AB}} = {R_{AD}} + {R_3} = 66\\
I = \dfrac{{{U_{AB}}}}{{{R_{AB}}}} = \dfrac{{15}}{{11}}A
\end{array}\)
- K đóng:
Mạch gồm: \({R_1}\parallel {\rm{[}}{R_2}nt({R_4}\parallel {{\rm{R}}_3}){\rm{]}}\)
\(\begin{array}{l}
{R_{43}} = \dfrac{{{R_4}{R_3}}}{{{R_4} + {R_3}}} = 12\\
{R_{ADB}} = {R_2} + {R_{43}} = 102\\
{R_{AB}} = \dfrac{{{R_1}{R_{ADB}}}}{{{R_1} + {R_{ADB}}}} = \dfrac{{2040}}{{71}}\\
I = \dfrac{{{U_{AB}}}}{{{R_{AB}}}} = \dfrac{{213}}{{68}}A
\end{array}\)
b)
- K mở:
\(\begin{array}{l}
{R_{14}} = {R_1} + {R_4} = 60\\
{R_{AD}} = \dfrac{{{R_{14}}.{R_2}}}{{{R_{14}} + {R_2}}} = 36\\
{R_{AB}} = {R_{AD}} + {R_3} = 36 + {R_3}\\
I = \dfrac{{{U_{AB}}}}{{{R_{AB}}}} = \dfrac{{90}}{{36 + {R_3}}} \Rightarrow {I_4} = \dfrac{{{R_2}}}{{{R_2} + {R_{14}}}}I = \frac{{54}}{{36 + {R_3}}}
\end{array}\)
- K đóng:
\(\begin{array}{l}
{R_{43}} = \dfrac{{{R_4}{R_3}}}{{{R_4} + {R_3}}} = \dfrac{{20{R_3}}}{{20 + {R_3}}}\\
{R_{ADB}} = {R_2} + {R_{43}} = \dfrac{{20{R_3}}}{{20 + {R_3}}} + 90 = \dfrac{{1800 + 110{R_3}}}{{{R_3} + 20}}\\
{R_{AB}} = \dfrac{{{R_1}{R_{ADB}}}}{{{R_1} + {R_{ADB}}}} = \dfrac{{440{R_3} + 7200}}{{15{R_3} + 260}}\\
I = \dfrac{{{U_{AB}}}}{{{R_{AB}}}} = \dfrac{{90(15{R_3} + 260)}}{{440{R_3} + 7200}}\\
\Rightarrow {I_{ADB}} = \dfrac{{360({R_3} + 20)}}{{440{R_3} + 7200}} \Rightarrow {I_4}' = \dfrac{{360{R_3}}}{{440{R_3} + 7200}}\\
{I_4} = {I_4}' \Rightarrow {R_3} \approx 51,12
\end{array}\)
