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?
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AWave A leads wave B by 15°.
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BWave A lags wave B by 15°.
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CWave A leads wave B by 105°.
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DWave A lags wave B by 105°.
Answer
Correct Answer: Wave A leads wave B by 15°.
Explanation
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:
Identify earlier crossing: 45° (A) vs 60° (B).Compute phase difference: Δφ = 60° − 45° = 15°.Since A is earlier, A leads B by 15°.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°.