When the r.m.s value of a source of electricity supply is given as 240v, it means that the peak value of the supply is

Analyze the question We are given the r.m.s. (root mean square) value of an a.c. supply, 240 V, and asked for the peak value (V₀).

Concept For a sinusoidal a.c. supply, the r.m.s. value is the steady d.c. value that would produce the same heating effect. It is related to the peak value by:

V_rms = V₀ / √2, so V₀ = V_rms × √2

Solution

V₀ = 240 × √2 V₀ = 240 × 1.414 V₀ ≈ 339.4 V ≈ 340 V

Check the options

• A. 240 V is the r.m.s. value itself, not the peak.
• B. 340 V matches our calculation.
• C. 480 V would be 2 × 240, which is the peak-to-peak mistake or a wrong factor.
• D. 57600 V is 240², which has no meaning here.

Tip Remember "peak is bigger than r.m.s. by about 1.4". Quick check: 240 × 1.4 ≈ 336, so the closest option is 340 V. Also, Nigerian mains is 240 V r.m.s., so the peak of about 340 V is a useful number to remember.