Question

The reactive power demanded by a circuit element will be zero when the phase difference between the current passing through it and the voltage across it becomes equal to

• A. zero degree
• B. \( \pm 45 \) degrees
• C. \( \pm 90 \) degrees
• D. \( \pm 180 \) degrees

Hint:

Zero reactive power occurs when the voltage and current are in phase (i.e., \( \theta = 0^\circ \) or \( 180^\circ \)).

Answer 1

The Correct Option is A

Think of reactive power as the "wasted" oscillating power that sloshes back and forth between source and load without doing net work — it's associated purely with voltage and current being out of step. For a purely resistive load, voltage and current rise and fall together in perfect step (in phase), so there's no oscillating exchange at all.

1. Zero degree: Voltage and current perfectly in step means all the delivered power is real, useful power — no reactive component exists, matching the requirement of zero reactive power.
2. \( \pm45^\circ \): A partial phase shift like this still leaves some out-of-step behavior between voltage and current, so some reactive power still exists.
3. \( \pm90^\circ \): This is the extreme case where voltage and current are entirely out of step (as in a pure inductor or capacitor) — here ALL the power is reactive, the opposite of what's asked.
4. \( \pm180^\circ \): This describes current running exactly opposite to voltage, which is not the standard resistive condition being tested here.

The in-phase condition is what makes an element demand purely real power with no reactive component.

Therefore, the correct answer is zero degree.

Answer 2

We can also see this from complex power, \( S = P + jQ \), where \( P = VI\cos\theta \) is real (active) power and \( Q = VI\sin\theta \) is reactive power. For \( Q \) to be exactly zero, the complex power \( S \) must lie entirely on the real axis, meaning the impedance of the element has zero reactive (imaginary) part — i.e., the element is purely resistive with current and voltage perfectly aligned. Let's check each option against this complex-power picture.

1. Zero degree: A 0° phase difference places \( S \) entirely on the positive real axis, exactly the purely-resistive, zero-reactive-power case.
2. \( \pm45^\circ \): This places \( S \) partway between the real and imaginary axes, so both real and reactive power exist together, not zero reactive power alone.
3. \( \pm90^\circ \): This places \( S \) entirely on the imaginary axis (all reactive, no real power) — the complete opposite of the zero-reactive-power condition being asked about.
4. \( \pm180^\circ \): This places \( S \) on the negative real axis, an atypical condition for a standard load element and not the case usually intended by this question.

The complex-power decomposition confirms zero reactive power corresponds to a 0° phase difference.

Therefore, the correct answer is zero degree.