Đáp án:
\({Z_L} = 500\left( \Omega \right)\)
Giải thích các bước giải:
Hệ số công suất: \(\cos \varphi = \dfrac{R}{Z} = \dfrac{R}{{\sqrt {{R^2} + {{\left( {{Z_L} - {Z_C}} \right)}^2}} }} = \dfrac{{\sqrt 2 }}{2}\)
\( \Leftrightarrow \dfrac{{{R^2}}}{{{R^2} + {{\left( {{Z_L} - {Z_C}} \right)}^2}}} = \dfrac{1}{2} \Leftrightarrow 2{{\rm{R}}^2} = {R^2} + {\left( {{Z_L} - {Z_C}} \right)^2}\)
\( \Leftrightarrow {\left( {{Z_L} - {Z_C}} \right)^2} = {R^2} \Leftrightarrow \left[ \begin{array}{l}{Z_L} - {Z_C} = R\\{Z_L} - {Z_C} = - R\end{array} \right.\)
\( \Leftrightarrow \left[ \begin{array}{l}{Z_L} = R + {Z_C} = 300 + 200 = 500\left( \Omega \right)\\{Z_L} = {Z_C} - R = 200 - 300 = - 100\left( \Omega \right)\,\left( L \right)\end{array} \right.\)
