An alternating e.m.f. of frequency v = frac{1 | vedclass

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(B) The given frequency $v = \frac{1}{2\pi \sqrt{LC}}$ corresponds to the resonant frequency of a series $LCR$ circuit.At resonance,the inductive reac

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The current in the circuit is in phase with the applied $e.m.f.$ and the voltage across $R$ equals this applied $e.m.f.$

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(B) The given frequency $v = \frac{1}{2\pi \sqrt{LC}}$ corresponds to the resonant frequency of a series $LCR$ circuit.At resonance,the inductive reactance $X_L = \omega L$ is equal to the capacitive reactance $X_C = \frac{1}{\omega C}$.Consequently,the net reactance $X = X_L - X_C = 0$.The impedance of the circuit $Z = \sqrt{R^2 + (X_L - X_C)^2}$ reduces to $Z = R$.Since the impedance is purely resistive,the current in the circuit is in phase with the applied $e.m.f.$Also,the voltage drop across the inductor and capacitor cancel each other out $(V_L + V_C = 0)$,meaning the entire applied $e.m.f.$ appears across the resistor $R$.

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

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