Question

For the following peak or rms values of some important sine waves, calculate the corresponding other value:

(a) 117 V rms, a household-power voltage in North America
(b) 33.9 V peak, a somewhat common peak voltage in rectifier circuits
(c) 220 V rms, a household-power voltage in parts of Europe
(d) 220 kV rms, a high-voltage transmission-line voltage in North America

Answer 1

A) V_peak ≈ 165 V

B) V_rms ≈ 24 V

C) V_peak ≈ 311 V

D) V_peak ≈ 311 KV

Step-by-step explanation:

Formula for RMS value is given as;

V_rms = V_peak/√2

Formula for peak value is given as;

V_peak = V_rms x √2

A) At RMS value of 117 V, peak value would be;

V_peak = 117 x √2

V_peak = 165.46 V

V_peak ≈ 165 V

B) At peak value of 33.9 V, RMS value would be;

V_rms = 33.9/√2

V_rms = 23.97 V

V_rms ≈ 24 V

C) At RMS value of 220 V, peak value is;

V_peak = 220 × √2

V_peak = 311.13 V

V_peak ≈ 311 V

D) At RMS value of 220 KV, peak value is;

V_peak = 220 × √2

V_peak = 311.13 KV

V_peak ≈ 311 KV