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

Step 1: Understanding reactive power.
Reactive power \( Q \) is given by \( Q = V I \sin \theta \), where \( \theta \) is the phase difference between voltage and current.
Step 2: Condition for zero reactive power.
For reactive power to be zero, \( \sin \theta = 0 \), which occurs when \( \theta = 0^\circ \) or \( 180^\circ \).
Step 3: Conclusion.
Thus, the reactive power is zero when the phase difference is 0° or 180°, which corresponds to option (A).

Answer 2

Reactive power is given by \( Q = VI\sin\theta \), where \( \theta \) is the phase difference between the voltage and current. For an element to demand zero reactive power, this expression must vanish, i.e., \( \sin\theta = 0 \). Let's check each option to see which phase difference makes this element behave as a purely resistive (real-power-only) load.

1. Zero degree: With \( \theta = 0^\circ \), the current is exactly in phase with the voltage (a purely resistive element), so \( \sin0^\circ = 0 \) and reactive power is indeed zero.
2. \( \pm45^\circ \): Here \( \sin(\pm45^\circ) = \pm0.707 \neq 0 \), so this phase difference still produces a non-zero reactive power.
3. \( \pm90^\circ \): This is the case of a purely reactive element (inductor or capacitor), where \( \sin(\pm90^\circ) = \pm1 \), giving the maximum possible reactive power, not zero.
4. \( \pm180^\circ \): While \( \sin(180^\circ)=0 \) mathematically, this corresponds to current exactly out of phase with voltage, an unusual condition not typically associated with a standard passive circuit element drawing power in the normal sense.

The condition \( \sin\theta = 0 \) at \( \theta = 0^\circ \) describes the standard, physically expected case of a purely resistive element demanding zero reactive power.

Therefore, the correct answer is zero degree.