R1=2R2=50căn 3 ôm

Ta có:
\(tan \varphi _{R_2 L} = \frac{Z_L}{R_2} = \frac{Z_L}{25\sqrt{3}} = 3 x\)
\(tan \varphi _{AB} = \frac{Z_L}{R_1 + R_2} = \frac{Z_L}{75\sqrt{3}} = x\)
Mặt khác:
\(\varphi = \varphi _{RL} - \varphi _{AB} \Leftrightarrow tan (\varphi _{RL} - \varphi _{AB}) = \frac{3 x - x}{1 + 3x.x} = \frac{2 x}{1 + 3x^2} = \frac{2}{\frac{1}{x} + 3 x} = \frac{2}{y}\)

\(y = \frac{1}{x} + 3 x \Rightarrow y' = \frac{- 1}{x^2} + 3\)

\(y' = 0 \Leftrightarrow 3 x^2 - 1 = 0 \Leftrightarrow \bigg \lbrack \begin{matrix} x = \frac{\sqrt{3}}{3}\\ x = - \frac{\sqrt{3}}{3}\end{matrix}\)
Khi \(x = \frac{\sqrt{3}}{3}\) thì \(y_{max}\Leftrightarrow \varphi _{max}\)
\(\Rightarrow tan \varphi _{R_2 L} = \frac{Z_L}{R_2} = \sqrt{3}\Leftrightarrow Z_L = 75 \Omega \Leftrightarrow L = \frac{3 \pi}{4}\)