Question

A complex wave of r.m.s. value 240 V has 20% 3rd harmonic content, 5% 5th harmonic content and 2% 7th harmonic content. Find the r.m.s. value of the fundamental and of each harmonic.

Answer 1

Let V₁, V₃, V₅ and V₇ be the r.m.s. values of the fundamental and harmonic voltages. 

Then V₃ = 0.2 V₁ ; V₅ = 0.05 V₁ and V₇ = 0.02 V₁ 

240 = (V₁² + V₃² + V₅² + V₇²)^1/2 

∴ 240 = [V₁² + (0.2 V₁)² + (0.05 V₁)² + (0.02 V₁)²]^1/2 

∴ V₁ = 235 V ; V₃ = 0.2 × 235 = 47V 

V₅ = 0.05 × 235 = 11.75 V ; V₇ = 0.02 × 235 = 4.7V