AIIMS 2007 Physics Power in AC Circuits Assertion Reason Question

To analyze the given question, we need to evaluate both the assertion and the reason regarding a pure capacitor in an AC circuit.

Assertion: No power loss associated with pure capacitor in AC circuit.

Explanation: In an AC circuit, a pure capacitor does not dissipate power. The power associated with an AC circuit can be described using the formula:

$P = VI \cos(\phi)$

where:

• $P$ is the average power,
• $V$ is the voltage,
• $I$ is the current,
• $\phi$ is the phase difference between voltage and current.

For a pure capacitor, the voltage and current are out of phase by $90^\circ$ (or $\frac{\pi}{2}$ radians). This means that $\cos(90^\circ) = 0$. Therefore, the average power $P$ delivered by the capacitor is:

$P = VI \cos(90^\circ) = 0$

This indicates that there is no power loss in the form of heat or work done; the energy is stored temporarily in the electric field of the capacitor and returned to the circuit.

Reason: No current is flowing in this circuit.

Explanation: The statement about "no current flowing" is misleading. In a pure capacitor, while the voltage and current are indeed out of phase by $90^\circ$, it does not mean that the current is zero. Instead, the current is given by:

$I(t) = C \frac{dV(t)}{dt}$

where $C$ is the capacitance and $V(t)$ is the instantaneous voltage across the capacitor. In an AC circuit, where voltage varies sinusoidally, the current will also vary sinusoidally, but it will be $90^\circ$ out of phase with the voltage. Thus, while there is current flowing, it does not result in power loss.

Conclusion on the Options:

• Option A: Both Assertion and Reason are true and Reason is the correct explanation of Assertion. (Incorrect): The assertion is true, but the reason is misleading; current does flow in a capacitor in an AC circuit.

• Option B: Both Assertion and Reason are true but Reason is not the correct explanation of Assertion. (Incorrect): The assertion is true, but the reason is not true since current does flow in the circuit.

• Option C: Assertion is true but Reason is false. (Correct): The assertion holds true as there is no power loss in a pure capacitor, while the reason is false since current does flow.

• Option D: Both Assertion and Reason are false. (Incorrect): The assertion is true.

Summary:

Thus, the correct answer is C: the assertion is true that there is no power loss associated with a pure capacitor in an AC circuit, while the reason provided is false because current does indeed flow in the circuit, even though it leads to zero average power dissipation.