Hai cuộn dây có ${R_1},{L_1},{R_2},{L_2}$  mắc n...

C

- Hướng dẫn giải

$\begin{array}{l} \left\{ \begin{array}{l} U = \sqrt {U_{{L_1}}^2 + U_{{R_1}}^2}  + \sqrt {U_{{L_2}}^2 + U_{{R_2}}^2} \\ U = \sqrt {{{\left( {{U_{{R_1}}} + {U_{{R_2}}}} \right)}^2} + {{\left( {{U_{{L_1}}} + {U_{{L_2}}}} \right)}^2}}  \end{array} \right.\\  \Rightarrow U_{{L_1}}^2 + U_{{R_1}}^2 + U_{{L_2}}^2 + U_{{R_2}}^2 + 2\sqrt {\left( {U_{{L_1}}^2 + U_{{R_1}}^2} \right)\left( {U_{{L_2}}^2 + U_{{R_2}}^2} \right)}  = {\left( {{U_{{R_1}}} + {U_{{R_2}}}} \right)^2} + {\left( {{U_{{L_1}}} + {U_{{L_2}}}} \right)^2} \end{array}$

$\begin{array}{l}  \Leftrightarrow \sqrt {\left( {U_{{L_1}}^2 + U_{{R_1}}^2} \right)\left( {U_{{L_2}}^2 + U_{{R_2}}^2} \right)}  = {U_{{R_1}}}{U_{{R_2}}} + {U_{{L_1}}}{U_{{L_2}}} \Leftrightarrow {\left( {{U_{L2}}{U_{R2}} - {U_{L1}}{U_{R1}}} \right)^2} = 0 \Leftrightarrow {U_{L2}}{U_{R2}} = {U_{L1}}{U_{R1}}\\  \Leftrightarrow {L_2}{R_2} = {L_1}{R_1} \end{array}$