The r.m.s value of a supply voltage is quoted at 200v. What is the approximate peak value of the voltage?

Analyze the question: You're given the r.m.s. (root mean square) value of an alternating voltage and asked for the peak value (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

Solution:

1. V_rms = 200 V
2. V_peak = 200 × √2
3. √2 ≈ 1.414
4. V_peak = 200 × 1.414 = 282.8 V ≈ 283 V

Checking the options:

• A. 200 V is the r.m.s. value itself, not the peak.
• B. 300 V is too high (it would need a factor of 1.5).
• C. 283 V matches our calculation.
• D. 250 V is too low (it would need a factor of 1.25).

The answer is C. 283 volts.

Tip: Remember "peak is bigger than r.m.s. by √2 (about 1.414)". For a quick check, multiply the r.m.s. value by 1.414. For example, Nigeria's 220 V mains has a peak of about 311 V. In the other direction, V_rms = 0.707 × V_peak. The same factor applies to current: I_peak = I_rms × √2.