Answer :

0.4473 (Range : 0.43 to 0.47)

Given :

I. v (t) = 230 √2 sinωt

II. i(t)= 10 sin (ωt- π/3) + 4 sin (3ωt- π/6) + 3 sin (5 ωt- π/3)

III. f = 50 Hz

IV. ω = 2π × 50 rad/sec.

Input power factor (IPF),

V ( t) |_RMS = 230 V,  i₁( t) |_RMS= 10/√2 A

Fundamental displacement factor (FDF) = cos ∅₁ = cos π/3= 1/2

Where, ∅₁ is the angle between voltage and fundamental component of current

i( t) |_RMS = √( 10/√2)² + ( 4/√2)² + ( 3/√2)² = 7.905 A

We know, IPF = Distortion factor Fundamental displacement factor
IPF = g × FDF

Also, g= i₁( t) |_RMS/ i( t) |_RMS = (10/√2)/ 7.905 = 0.8946

Therefore, IPF = 0.8946 × 0.5 = 0.4473

Hence, the correct answer is 0.4473