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The peak voltage of an ac supply is 300 V. _____ V is the value of the rms voltage.

Asked in GSEB Board August 2020 · RMS and mean values

(1) 212
(2) 173
(3) 423
(4) 269

Answer: (1) 212

Step-by-step solution

Given: peak voltage V₀=300 V.

Idea: for a sinusoidal supply Vᵣₘₛ=(V₀)/(√2)=0.707 V₀.

Vᵣₘₛ=(300)/(1.414)=212 V.

So the rms voltage is 212 V.

Why the other options are wrong

(2) 173=(300)/(√3): dividing by √3 instead of √2. The factor √2 comes from sin²ω t averaging to 1/2 over a cycle.
(3) 423=300×1.41: multiplying by √2 instead of dividing. The rms value of a sinusoid is always less than its peak.
(4) No single slip gives 269 V. Sanity check: the rms value is 0.707 of the peak, and 0.707×300=212 V.

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