Sine-wave characteristics: which option correctly defines the peak value of a sinusoidal waveform in electrical engineering?

Introduction / Context:
Signal specifications such as peak, peak-to-peak, and RMS values are ubiquitous in power systems and electronics. Misinterpreting these can lead to incorrect component ratings and analysis errors. The question focuses on the correct definition of the peak value of a sinusoid.

Given Data / Assumptions:

• The waveform is a pure sine wave.
• Standard engineering definitions apply (peak, peak-to-peak, RMS).
• Amplitude refers to instantaneous magnitude from the zero reference.

Concept / Approach:
The peak value (sometimes called the amplitude for symmetric sinusoids) is the largest instantaneous magnitude measured from zero. For a sine v(t) = V_peak * sin(ωt), the maximum is +V_peak and the minimum is −V_peak. RMS is V_peak / √2 ≈ 0.707 * V_peak, not 70.7% of “maximum” in the sense used by option (a).

Step-by-Step Solution:
Define peak value: the maximum magnitude reached by the waveform.Relate to RMS: V_RMS = V_peak / √2.Relate to peak-to-peak: V_pp = 2 * V_peak.Therefore, peak is simply the maximum positive or negative value reached.

Verification / Alternative check:
Consider v(t) = 10 sin(ωt): peak = 10, RMS ≈ 7.07, peak-to-peak = 20. These relationships highlight the distinctions among common measures.

Why Other Options Are Wrong:
70.7% of maximum: that statement describes RMS relative to peak, not the peak definition.90% of maximum: arbitrary and incorrect.1.41 times the maximum: 1.414 relates peak to RMS, but direction is reversed (peak = 1.414 * RMS).None of the above: incorrect because option (d) is correct.

Common Pitfalls:
Confusing RMS, average, and peak values; mixing peak and peak-to-peak ratings on datasheets.

Final Answer:
the maximum positive or negative value