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(C) In the given circuit,an inductor $L$ and a capacitor $C$ are connected in parallel to an $AC$ source. The ammeter $A_1$ measures the current throu

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$A_3$

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(C) In the given circuit,an inductor $L$ and a capacitor $C$ are connected in parallel to an $AC$ source. The ammeter $A_1$ measures the current through the inductor $(I_L = V/X_L)$,and $A_2$ measures the current through the capacitor $(I_C = V/X_C)$. The ammeter $A_3$ measures the total current from the source ($I = I_L + I_C$ in phasor form).At resonance,the inductive reactance $X_L = \omega L$ is equal to the capacitive reactance $X_C = 1/(\omega C)$.Thus,the magnitudes of the currents are equal: $|I_L| = |I_C|$.However,in a parallel $LC$ circuit,the current through the inductor lags the voltage by $90^\circ$ and the current through the capacitor leads the voltage by $90^\circ$.Therefore,the currents $I_L$ and $I_C$ are $180^\circ$ out of phase.The total current $I = I_L + I_C = I_L - I_C = 0$ (since $|I_L| = |I_C|$).Thus,the ammeter $A_3$ will show a zero reading.

If the frequency of the $AC$ supply is equal to the resonant frequency,which ammeter will show zero reading?

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