Phase comparison: Sine wave A has a positive-going zero crossing at 45°, while sine wave B crosses zero positively at 60°. Which statement about their phase relationship is correct?

Introduction / Context:
Phase lead/lag is central to AC analysis. The positive-going zero crossing is a clear reference marker: the waveform that crosses zero earlier in angle is said to lead the other. This question compares two given crossing angles.

Given Data / Assumptions:

• Wave A positive-going zero crossing at 45°.
• Wave B positive-going zero crossing at 60°.
• Both are sinusoidal and at the same frequency.

Concept / Approach:

If wave A reaches a reference point earlier (smaller angle), A leads B by the difference in their angles. If A reached later (larger angle), it would lag. Here, the angles are measured consistently from the same reference.

Step-by-Step Solution:

Verification / Alternative check:

Visualize rotating phasors: A's phasor angle is 15° ahead of B at any instant for equal frequencies; equivalently, B lags A by 15°.

Why Other Options Are Wrong:

‘‘Lags by 15°’’ reverses the relationship. 105° differences are incorrect and exceed the small offset implied by the given crossings.

Common Pitfalls:

Swapping lead and lag; subtracting in the wrong order; confusing negative-going with positive-going crossings.

Final Answer:

Wave A leads wave B by 15°.