AIIMS 2003 Physics LC Circuits MCQ Question

In an ideal parallel LC circuit, we have an inductor (L) and a capacitor (C) connected in parallel. When the capacitor is charged by a direct current (DC) source and then disconnected, the behavior of the circuit changes significantly. Let's analyze the situation.

Explanation of the Correct Answer (D: Oscillates Instantaneously)

Once the DC source is disconnected, the capacitor will begin to discharge through the inductor. The charged capacitor will create a current flow through the inductor, which will generate a magnetic field. According to Lenz's law, this magnetic field will oppose any change in current, leading to oscillations in the circuit.

The fundamental principle governing these oscillations is given by the formula for the natural frequency of oscillation in an LC circuit:

$\omega = \frac{1}{\sqrt{LC}}$

Where:

• $\omega$ is the angular frequency of oscillation,
• $L$ is the inductance,
• $C$ is the capacitance.

The current and voltage in the circuit will oscillate sinusoidally. The mathematical representation of the current $I(t)$ in the circuit can be expressed as:

$I(t) = I_0 \sin(\omega t)$

Where:

• $I_0$ is the maximum current,
• $t$ is time,
• $\omega$ is the angular frequency as defined above.

The oscillation occurs because the energy stored in the electric field of the capacitor is converted into magnetic energy in the inductor and then back into electric energy, creating a continuous exchange between the two.

Clarification of Incorrect Options

A) Becomes zero instantaneously

• This option is incorrect because when the capacitor discharges, the current does not drop to zero instantly. Instead, it begins to flow due to the oscillation between the capacitor and the inductor.

B) Grows monotonically

• This option is incorrect because the current does not grow over time; rather, it oscillates. In a growing monotonically scenario, the current would continue to increase without any decrease, which is not the case here.

C) Decays monotonically

• This option implies that the current decreases over time until it reaches zero. In reality, the current oscillates back and forth indefinitely (in an ideal scenario without resistance), rather than just decaying.

Conclusion

In summary, when the charged capacitor in an ideal parallel LC circuit is disconnected from the DC source, the current oscillates due to the exchange of energy between the capacitor and the inductor. The correct answer is D, as the circuit demonstrates harmonic oscillations rather than a simple increase or decrease in current.