Calculate the peak voltage of a mains supply of r.ms. value 220V.

Analyze the question: We are given the r.m.s. (root mean square) value of an a.c. mains supply and asked for the peak (maximum) voltage.

Concept: For a sinusoidal a.c. supply, the r.m.s. value is related to the peak value by:

V_rms = V_peak / √2, so V_peak = V_rms × √2

The r.m.s. value is the steady d.c. voltage that would produce the same heating effect in a resistor as the a.c.

Solution:

V_peak = 220 × √2 V_peak = 220 × 1.414 V_peak ≈ 311.1 V

Check the options:

• A (121 V) and B (156 V) are too small, because the peak must be larger than the r.m.s. value. They come from dividing by √2 or by 2 instead of multiplying.
• C (225 V) and D (240 V) are only slightly above 220 V, which does not match a factor of 1.414.
• E (311 V) matches our calculation.

Answer: E. 311 V

Tip: Remember that the peak is always bigger than the r.m.s. value, by a factor of about 1.414. Quick check: 220 × 1.4 = 308, so the answer should be a little above 300 V. Also, 240 V mains gives a peak of about 340 V, and 220 V gives about 311 V. Both are common in exams.