Household mains supply is typically specified as 230 V AC (rms). For such a sinusoidal source, what is the peak voltage Vp delivered to a resistive appliance?

Introduction:AC mains specifications such as 230 V refer to rms (root-mean-square) values, which indicate the DC equivalent heating effect. Converting between rms and peak values for a sine wave is a routine task in power electronics and safety calculations.

Given Data / Assumptions:

• Sine wave AC at Vrms = 230 V.
• Resistive load; no distortion assumed.
• We seek the peak value Vp.

Concept / Approach:For a sinusoidal voltage: Vrms = Vp / √2, hence Vp = Vrms * √2. This relation arises from averaging the square of a sinusoid over a full cycle.

Step-by-Step Solution:Use Vp = Vrms * √2Compute √2 ≈ 1.414Vp = 230 V * 1.414 ≈ 325.22 VRounded appropriately: Vp ≈ 325 V

Verification / Alternative check:Peak-to-peak value Vpp = 2 * Vp ≈ 650 V, which is consistent with insulation rating considerations. Many appliance and rectifier designs reference these peak values when sizing components.

Why Other Options Are Wrong:

• 163 V: This is 230 / √2 (the peak of a 115 Vrms system, not 230 Vrms).
• 230 V: The rms value, not the peak.
• 480 V and 650 V: 650 V is closer to peak-to-peak, not peak; 480 V is unrelated.

Common Pitfalls:

• Confusing peak with rms or peak-to-peak.
• Forgetting that real mains may deviate slightly; calculations assume nominal values.

Final Answer:325 V