In a circuit,L,C,and R are connected in serie | vedclass

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(A) The phase angle $\phi$ in an $LCR$ series circuit is given by $	an \phi = \frac{X_C - X_L}{R}$,where the current leads the voltage when $X_C > X_

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$\frac{1}{2 \pi f(2 \pi f L+R)}$

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(A) The phase angle $\phi$ in an $LCR$ series circuit is given by $	an \phi = \frac{X_C - X_L}{R}$,where the current leads the voltage when $X_C > X_L$.Given that the current leads the voltage by $45^{\circ}$,we have $\phi = -45^{\circ}$ (or using the magnitude,$	an 45^{\circ} = \frac{X_C - X_L}{R}$).Substituting $X_C = \frac{1}{\omega C}$ and $X_L = \omega L$:$1 = \frac{\frac{1}{\omega C} - \omega L}{R}$$R = \frac{1}{\omega C} - \omega L$$\frac{1}{\omega C} = R + \omega L$$C = \frac{1}{\omega(R + \omega L)}$Since $\omega = 2 \pi f$,we get:$C = \frac{1}{2 \pi f(R + 2 \pi f L)}$

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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