Power of the following circuit will be zero.

Question

Examoogle · Accepted Answer

Both B and C

Explanation: In an AC circuit, the average power dissipated is given by $P = VI \cos\phi$. For purely inductive or purely capacitive circuits, the phase angle $\phi$ between voltage and current is $90^\circ$ or $-90^\circ$, making the power factor $\cos(90^\circ) = 0$, resulting in zero real power consumption.

Working Principle: In pure reactive elements (inductors or capacitors), energy is stored in the magnetic or electric field during one quarter of the cycle and returned to the source in the next quarter. Since the net energy exchange over a complete cycle is zero, the real power (active power) consumed is zero.

Key Formulas: $P = VI \cos \phi$ — Formula for real power in an AC circuit; $\phi = 90^\circ$ — Phase shift for purely reactive components

Key Points: Purely resistive circuits have a power factor of 1, resulting in maximum power dissipation.; Reactive power ($Q = VI \sin \phi$) is non-zero in purely reactive circuits, but real power ($P$) is zero.; Real power represents the actual work done or heat dissipated in the circuit.

Advantages: Ideal inductors and capacitors are lossless in theory.; Allows for efficient energy storage without heat dissipation.

Disadvantages: Real components always have parasitic resistance (ESR), so $P$ is never exactly zero in practice.; High reactive power can lead to poor grid power factor.

Applications: Filter design in electronic circuits.; Phase shifting networks and resonant circuits.

Additional Info: Purely resistive circuit dissipates power as heat: $P = I^2R$.. Option A is incorrect because resistive circuits have unity power factor and consume real power.

Answer: D is correct — Both purely inductive and purely capacitive circuits have a phase difference of $90^\circ$ between voltage and current, leading to a power factor of zero.

Exam Tip: Always remember that in AC analysis, real power is only associated with resistive elements; inductors and capacitors only cycle energy back and forth.

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