Hai cuộn dây có ({R_1},{L_1},{R_2},{L_2})  mắc nối tiếp vào mạng điện xoay chiều (u = Usqrt 2 cosomega tleft( V ight))

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

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