Đáp án:

a) \({R_1} = \dfrac{{{R_2}}}{2}\)

b) \(\left\{ \begin{array}{l}
{R_1} = 15\Omega \\
{R_2} = 30\Omega 
\end{array} \right.\)

Giải thích các bước giải:

a) Ta có: 

\(\begin{array}{l}
\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{{\dfrac{{{\rho _1}{l_1}}}{{{S_1}}}}}{{\dfrac{{{\rho _2}{l_2}}}{{{S_2}}}}} = \dfrac{{{\rho _1}}}{{{\rho _2}}}.\dfrac{{{l_1}}}{{{l_2}}}.\dfrac{{{S_2}}}{{{S_1}}} = \dfrac{{0,4}}{{0,5}}.\dfrac{1}{8}.\dfrac{{2,5}}{{0,5}} = \dfrac{1}{2}\\
 \Rightarrow {R_1} = \dfrac{{{R_2}}}{2}
\end{array}\)

b) Ta có: 

\(\begin{array}{l}
{R_1} + {R_2} = \dfrac{U}{I} = \dfrac{{45}}{1} = 45\Omega \\
 \Rightarrow \left\{ \begin{array}{l}
{R_1} = 15\Omega \\
{R_2} = 30\Omega 
\end{array} \right.
\end{array}\)