Power circuit of the following circuit will be zero

Question

Examoogle · Accepted Answer

both b and c

Explanation: In an ideal AC circuit, the average power (or real power) consumed by purely inductive or purely capacitive loads is zero. This occurs because these components store energy in their magnetic or electric fields during one half-cycle and return it to the source during the next, resulting in zero net work done over a complete cycle.

Working Principle: The instantaneous power in an AC circuit is given by $p = vi$. For a purely reactive element, the current and voltage are in quadrature (90° phase difference), i.e., $v = V_m \sin(\omega t)$ and $i = I_m \sin(\omega t \pm 90^\circ)$. The integration of power over one time period $T$ results in zero because $\int_{0}^{T} \sin(\omega t)\cos(\omega t) dt = 0$.

Key Formulas: $P = VI \cos(\phi)$ — Formula for real power in an AC circuit; $Q = VI \sin(\phi)$ — Formula for reactive power (measured in VAR)

Key Points: Purely resistive circuits have a power factor of 1, consuming maximum real power.; Purely reactive components (inductors/capacitors) have a power factor of 0.; Real power ($P$) is measured in Watts (W), while reactive power ($Q$) is measured in VAR.; Total power is represented as Complex Power $S = P + jQ$.

Advantages: Ideal reactive components do not generate heat (no $I^2R$ loss).; Essential for power factor correction using capacitor banks.

Disadvantages: Purely reactive components are theoretical; real-world inductors have internal winding resistance.; High reactive power can lead to voltage drops and reduced transmission line efficiency.

Applications: Inductors used in filtering and energy storage.; Capacitors used in power factor correction and timing circuits.

Additional Info: The term 'power circuit' in the question refers to the 'average active power' consumed.. Option A (resistive) consumes $P = I^2R$ power, which is never zero for non-zero current.. Option B and C result in zero average power because the phase angle $\phi$ is $\pm 90^\circ$.

Answer: D is correct — Both purely inductive and purely capacitive circuits have a phase angle of $90^\circ$, leading to a power factor of zero and consequently zero real power consumption.

Exam Tip: Always remember that in AC circuits, the power factor is $\cos(\phi)$. If the circuit is purely reactive, $\phi = 90^\circ$, and $\cos(90^\circ) = 0$, meaning no real power is consumed.

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