Lời giải:Ta có: \(\overrightarrow{{{U}_{AN}}}\bot \overrightarrow{{{U}_{MB}}}\)
\(\Rightarrow \frac{{{Z}_{C}}}{R}.\frac{{{Z}_{L}}-{{Z}_{C}}}{r}=1\Leftrightarrow R.r={{Z}_{C}}.{{Z}_{L}}-Z_{C}^{2}\Rightarrow R.r=\frac{1}{C\omega }.L\omega -\frac{1}{{{C}^{2}}.{{\omega }^{2}}}\)
Đặt:
\(\left\{ \begin{array}{l}
R = y\\
\frac{1}{{{\omega ^2}}} = x
\end{array} \right. \Rightarrow y = b - a \Rightarrow \left\{ \begin{array}{l}
b = \frac{L}{{C.r}}\\
a = \frac{1}{{{C^2}.r}}
\end{array} \right.\)
Từ đồ thị (chuẩn hóa \(\frac{1}{{{\omega }^{2}}}\)) suy ra:
\(\begin{array}{l}
y = 40 \Rightarrow x = 6 \Rightarrow 40 = b - 6.a\\
y = 80 \Rightarrow x = 5 \Rightarrow 80 = b - 5.a\\
\Rightarrow \left\{ \begin{array}{l}
b = 280\\
a = 40
\end{array} \right. \Rightarrow \frac{L}{{C.r}} = 280 \Rightarrow r = 4\Omega
\end{array}\)
