A resistor R,an inductor L,and a capacitor C | vedclass

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(D) In an $LCR$ series circuit,the phase angle $\phi$ is given by $	an \phi = \frac{X_L - X_C}{R}$.For the current to lag behind the voltage,the phas

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$n > n_r$

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(D) In an $LCR$ series circuit,the phase angle $\phi$ is given by $	an \phi = \frac{X_L - X_C}{R}$.For the current to lag behind the voltage,the phase angle $\phi$ must be positive,which implies $X_L > X_C$.Substituting the expressions for reactances: $\omega L > \frac{1}{\omega C}$.This simplifies to $\omega^2 > \frac{1}{LC}$,or $\omega > \frac{1}{\sqrt{LC}}$.Since $\omega = 2\pi n$ and the resonant frequency $n_r = \frac{1}{2\pi \sqrt{LC}}$,the condition becomes $2\pi n > 2\pi n_r$,which simplifies to $n > n_r$.

$A$ resistor $R$,an inductor $L$,and a capacitor $C$ are connected in series to an oscillator of frequency $n$. If the resonant frequency is $n_r$,then the current lags behind the voltage when:

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