In an LCR series circuit, an alternating volt | vedclass

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(C) In an $LCR$ series circuit, the phase angle $\phi$ is given by $	an \phi = \frac{X_C - X_L}{R}$.Given that the current leads the voltage by $45^{

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$\frac{1 + 2\pi FCR}{4\pi^2 F^2 C}$

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(C) In an $LCR$ series circuit, the phase angle $\phi$ is given by $	an \phi = \frac{X_C - X_L}{R}$.Given that the current leads the voltage by $45^{\circ}$, the phase angle $\phi = -45^{\circ}$.Thus, $	an(-45^{\circ}) = \frac{X_C - X_L}{R} \implies -1 = \frac{X_C - X_L}{R}$.This gives $X_L - X_C = R$.Substituting $X_L = 2\pi FL$ and $X_C = \frac{1}{2\pi FC}$, we get $2\pi FL - \frac{1}{2\pi FC} = R$.$2\pi FL = R + \frac{1}{2\pi FC} = \frac{2\pi FCR + 1}{2\pi FC}$.Solving for $L$, we get $L = \frac{1 + 2\pi FCR}{4\pi^2 F^2 C}$.

In an $LCR$ series circuit, an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^{\circ}$. The value of $L$ is

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