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In a circuit, $L, C$ and $R$ are connected in series with an alternating voltage source of frequency $f$. The current leads the voltage by $45^{\circ}$. The value of $C$ is
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Verified Answer
The correct answer is:
$\frac{1}{2 \pi f(2 \pi f L-R)}$
\(\begin{aligned}
& \tan \phi=\frac{X_C-X_L}{R} \\
& \tan \left(\frac{\pi}{4}\right)=\frac{\frac{1}{\omega C}-\omega L}{R} \\
& R=\frac{1}{\omega C}-\omega L \\
& (R+2 \pi f L)=\frac{1}{2 \pi f C} \\
& \text {or } C=\frac{1}{2 \pi f(R+2 \pi f L)}
\end{aligned}\)
& \tan \phi=\frac{X_C-X_L}{R} \\
& \tan \left(\frac{\pi}{4}\right)=\frac{\frac{1}{\omega C}-\omega L}{R} \\
& R=\frac{1}{\omega C}-\omega L \\
& (R+2 \pi f L)=\frac{1}{2 \pi f C} \\
& \text {or } C=\frac{1}{2 \pi f(R+2 \pi f L)}
\end{aligned}\)
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