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In an a.c. circuit the peak value of voltage is 141.4 V. Then the rms value of voltage is ______ volt.

Asked in GSEB Board March 2016 · RMS and mean values

• (1) 199.5
• (2) 100
• (3) 70.55
• (4) 141.4

Step-by-step solution

Why the other options are wrong

• (1) This is close to 141.4×√2≈200: the peak multiplied by √2 instead of divided. The rms value of a sinusoid is always smaller than its peak.
• (3) This is close to (141.4)/2=70.7: dividing by 2 instead of by √2. The rms value is 0.707 of the peak, not half of it.
• (4) 141.4 is the peak value itself. For a sinusoidal voltage the rms value is (V₀)/(√2), smaller than the peak.

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