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Câu hỏi: Mạch RLC nối tiếp có $\mathrm{R}=100 \Omega, \mathrm{L}=2 / \pi(\mathrm{H}), \mathrm{f}=50 \mathrm{~Hz}$. Biết i nhanh pha hơn u một góc $\pi / 4$ rad.
Điện dung $C$ có giá trị là
A. $\boldsymbol{C}=\dfrac{500}{3 \pi}$
B. $\boldsymbol{C}=\dfrac{100}{\pi} \mu \mathrm{F}$
C. $\boldsymbol{C}=\dfrac{100}{3 \pi} \mu \mathrm{F}$
D. $\boldsymbol{C}=\dfrac{\mathbf{5 0 0}}{\pi} \mu \mathrm{F}$
Điện dung $C$ có giá trị là
A. $\boldsymbol{C}=\dfrac{500}{3 \pi}$
B. $\boldsymbol{C}=\dfrac{100}{\pi} \mu \mathrm{F}$
C. $\boldsymbol{C}=\dfrac{100}{3 \pi} \mu \mathrm{F}$
D. $\boldsymbol{C}=\dfrac{\mathbf{5 0 0}}{\pi} \mu \mathrm{F}$
$
\begin{aligned}
& \omega=2 \pi \mathrm{f}=2 \pi \cdot 50=100 \pi(\mathrm{rad} / \mathrm{s}) \\
& Z_{\mathrm{L}}=\omega \mathrm{L}=100 \pi \cdot \dfrac{2}{\pi}=200 \Omega \\
& \tan \varphi=\dfrac{Z_L-Z_C}{R} \Rightarrow \tan \left(-\dfrac{\pi}{4}\right)=\dfrac{200-Z_C}{100} \Rightarrow Z_{\mathrm{C}}=300 \Omega \\
& \mathrm{C}=\dfrac{1}{\omega Z_C}=\dfrac{1}{100 \pi \cdot 300} \mathrm{~F}=\dfrac{100}{3 \pi} \mu \mathrm{F} .
\end{aligned}
$
\begin{aligned}
& \omega=2 \pi \mathrm{f}=2 \pi \cdot 50=100 \pi(\mathrm{rad} / \mathrm{s}) \\
& Z_{\mathrm{L}}=\omega \mathrm{L}=100 \pi \cdot \dfrac{2}{\pi}=200 \Omega \\
& \tan \varphi=\dfrac{Z_L-Z_C}{R} \Rightarrow \tan \left(-\dfrac{\pi}{4}\right)=\dfrac{200-Z_C}{100} \Rightarrow Z_{\mathrm{C}}=300 \Omega \\
& \mathrm{C}=\dfrac{1}{\omega Z_C}=\dfrac{1}{100 \pi \cdot 300} \mathrm{~F}=\dfrac{100}{3 \pi} \mu \mathrm{F} .
\end{aligned}
$
Đáp án C.