Đáp án:

a) \(50\sqrt 5 \Omega \)

b) \(\dfrac{4}{{\sqrt 5 }}\left( A \right)\)

c) \(i = \dfrac{4}{{\sqrt 5 }}\cos \left( {100\pi t + 0,584} \right)\)

Giải thích các bước giải:

a) Ta có: 

\(\begin{array}{l}
{Z_L} = \omega L = 100\pi .\dfrac{{1,5}}{\pi } = 150\Omega \\
{Z_C} = \dfrac{1}{{\omega C}} = \dfrac{1}{{100\pi .\dfrac{{{{10}^{ - 4}}}}{\pi }}} = 100\Omega \\
Z = \sqrt {{R^2} + {{\left( {{Z_L} - {Z_C}} \right)}^2}}  = 50\sqrt 5 \Omega 
\end{array}\)

b) Ta có: 

\(I = \dfrac{U}{Z} = \dfrac{{200}}{{50\sqrt 5 }} = \dfrac{4}{{\sqrt 5 }}\left( A \right)\)

c) Ta có: 

\(\begin{array}{l}
\cos \varphi  = \dfrac{R}{Z} = \dfrac{{100}}{{50\sqrt 5 }} \Rightarrow \varphi  = 0,463\left( {rad} \right)\\
 \Rightarrow {\varphi _i} = {\varphi _u} - 0,463 = 0,584\left( {rad} \right)\\
 \Rightarrow i = \dfrac{4}{{\sqrt 5 }}\cos \left( {100\pi t + 0,584} \right)
\end{array}\)