Đặt điện áp xoay chiều u có giá trị hiệu dụng khôn...

A

- Hướng dẫn giải

Khi đó: \({i_1} = {I_0}\cos \left( {\varphi - \alpha } \right) = {I_0}\cos \frac{{3\varphi }}{2}\)

\({i_2} = {I_0}\cos \left( {\frac{{3\varphi }}{2} - 2\alpha } \right) = {I_0}\cos \frac{\varphi }{2}\)

\(\begin{array}{l} \Rightarrow \frac{{{i_1}}}{{{i_2}}} = \frac{{\cos \left( {3\varphi /2} \right)}}{{\cos \left( {\varphi /2} \right)}} = \frac{1}{3}\\ \Leftrightarrow \frac{{4{{\cos }^3}\left( {\varphi /3} \right) - 3\cos \left( {\varphi /2} \right)}}{{\cos \left( {\varphi /2} \right)}} = \frac{1}{3}\end{array}\)

\(\Leftrightarrow 4{\cos ^2}\left( {\frac{\varphi }{2}} \right) - 3 = \frac{1}{3}\)

\(\Leftrightarrow {\cos ^2}\left( {\frac{\varphi }{2}} \right) = \frac{5}{6} \Rightarrow \cos \frac{\varphi }{2} = \sqrt {\frac{5}{6}} \)

\(\Rightarrow \varphi \approx 0,84\left( {rad} \right)\)

\(\tan \varphi = \frac{{{Z_L}}}{R} \Rightarrow {Z_L} = 27\left( \Omega \right)\)

\(\Rightarrow L = \frac{{{Z_L}}}{\omega } = 0,21\left( M \right).\)