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With an alternating voltage source of frequency ' $\mathrm{f}$ ', inductor ' $\mathrm{L}$ ', capacitor ' $\mathrm{C}$ ' and resistance ' $R$ ' are connected in series. The voltage leads the current by $45^{\circ}$. The value of ' $L$ ' is $\left(\tan 45^{\circ}=1\right)$
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The correct answer is:
$\left(\frac{1+2 \pi f \mathrm{CR}}{4 \pi^2 \mathrm{f}^2 \mathrm{C}}\right)$
$\begin{aligned} & \quad \tan \phi=\frac{X_L-X_C}{R} \\ & \Rightarrow \tan 45^{\circ}=\left[\frac{2 \pi \mathrm{fL}-\frac{1}{2 \pi \mathrm{fC}}}{R}\right] \quad \ldots .\left(\because \phi=45^{\circ}\right) \\ & \quad R=\frac{(2 \pi \mathrm{f})^2 \mathrm{LC}-1}{2 \pi \mathrm{fC}} \\ & \therefore \quad L=\frac{2 \pi \mathrm{fCR}+1}{4 \pi^2 \mathrm{f}^2 \mathrm{C}}\end{aligned}$
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