Question

In the resonance condition, the current drawn from the source by a parallel resonant (L-C) circuit is:

• A. infinite
• B. zero
• C. fixed
• D. none of these

Hint:

At parallel resonance the two branch currents are equal and opposite, so the impedance is maximum and the line current is minimum.

Answer 1

The Correct Option is B

Step 1: Understand a parallel L-C circuit.
An inductor \( L \) and a capacitor \( C \) are joined in parallel across an AC source. The circuit resonates when the inductive reactance equals the capacitive reactance, \[ X_L = X_C \Rightarrow \omega L = \frac{1}{\omega C}. \]

Step 2: Behaviour of impedance at resonance.
For an ideal (lossless) parallel L-C circuit the net impedance becomes maximum (theoretically infinite) at resonance, because the currents in the two branches are equal in magnitude but opposite in phase and cancel in the main line. \[ Z_{parallel} = \infty \ (\text{ideal}). \]

Step 3: Apply Ohm's law for AC.
The line current supplied by the source is \[ I = \frac{V}{Z}. \] With \( Z \to \infty \), \[ I \to 0. \]

Step 4: Interpret.
A parallel resonant circuit is therefore called a rejector circuit: it draws essentially zero current from the source at resonance while a large current circulates internally between L and C.

Step 5: Eliminate the other options.
Infinite current happens in a series resonant circuit (impedance minimum), not parallel; hence (i) is wrong. The current is not merely fixed, so (iii) fails, and a definite answer exists so (iv) is unnecessary. Option (ii) is correct.
\[\boxed{I = 0}\]