A capacitor will be used on a 230 V, 50 Hz AC supply. What minimum peak-voltage rating should be specified for the capacitor to ensure safe operation?

Introduction / Context:
Capacitors used on sinusoidal AC must be rated for the maximum instantaneous voltage, not merely the RMS value. Exceeding the dielectric strength can cause breakdown, heating, and catastrophic failure. Therefore, selecting an appropriate peak-voltage rating is a basic but critical design step.

Given Data / Assumptions:

• Supply: 230 V RMS, 50 Hz sinusoid.
• Ideal capacitor; no waveform distortion.
• We seek the minimum peak (not RMS) voltage rating.

Concept / Approach:
For a pure sinusoid v(t) = V_max sin(ωt), the RMS value is V_rms = V_max / √2. Therefore V_max = √2 * V_rms. A device connected across the line must withstand at least this peak. In practice, designers add margin for transients (surges/spikes), but the theoretical minimum for a clean sinusoid is √2 times the RMS value.

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