The L-C-R circuit shown below is driven by an | vedclass

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(A) The circuit consists of a resistor $R$ in series with a parallel combination of an inductor $L$ and a capacitor $C$. At the given frequency $f = \

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The current through $R$ is zero.

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(A) The circuit consists of a resistor $R$ in series with a parallel combination of an inductor $L$ and a capacitor $C$. At the given frequency $f = \frac{1}{2 \pi \sqrt{L C}}$,the angular frequency is $\omega = 2 \pi f = \frac{1}{\sqrt{L C}}$. This is the resonant frequency of the $L-C$ parallel circuit. At this frequency,the inductive reactance $X_L = \omega L$ and capacitive reactance $X_C = \frac{1}{\omega C}$ are equal,i.e.,$X_L = X_C$. For a parallel $L-C$ circuit,the equivalent impedance $Z_{LC}$ is given by $\frac{1}{Z_{LC}} = \sqrt{(\frac{1}{X_L})^2 + (\frac{1}{X_C} - \frac{1}{X_L})^2}$ is not correct here; rather,the admittance $Y = \sqrt{(\frac{1}{R_{LC}})^2 + (\frac{1}{X_L} - \frac{1}{X_C})^2}$. Since $X_L = X_C$,the net reactance of the parallel $L-C$ combination becomes infinite $(Z_{LC} 	o \infty)$. Therefore,the parallel $L-C$ combination acts as an open circuit. Consequently,the current through the entire circuit,including the resistor $R$,becomes zero.

The $L-C-R$ circuit shown below is driven by an ideal $AC$ voltage source. At frequency $f=\frac{1}{2 \pi \sqrt{L C}}$,choose the correct statement.

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