AC waveform with DC offset: A sinusoid with an rms value of 12 V is superimposed on a steady 18 V DC level. What is the maximum (peak positive) value of the resulting voltage waveform?

Introduction / Context:
Many practical signals are an AC sine wave riding on a DC offset. To find the instantaneous maximum, you must combine the DC level with the positive peak of the sinusoid. This question checks comfort with rms–peak conversion and how offsets shift waveform extrema in electronics and instrumentation.

Given Data / Assumptions:

• Sine wave rms value: 12 V.
• DC offset (baseline): 18 V.
• Ideal sinusoid; standard rms–peak relation for sine applies.

Concept / Approach:
For a sine wave: V_peak = V_rms * sqrt(2). The waveform with offset has maximum value V_max = V_DC + V_peak and minimum value V_min = V_DC − V_peak. Only the maximum is asked here.

Step-by-Step Solution:

Verification / Alternative check:
Check the minimum for sanity: V_min = 18 − 16.97 ≈ 1.03 V > 0, consistent with a positive-offset waveform never going negative.

Why Other Options Are Wrong:

• 30 V: This ignores part of the AC peak contribution.
• 6 V or 0 V: Numerically inconsistent; these confuse rms/peak or ignore the DC offset entirely.

Common Pitfalls:

• Using V_rms directly instead of converting to peak.
• Adding peak-to-peak to DC instead of the single-sided peak.

Final Answer:
35 V