The voltage at the input of an AC-DC rectifier is given by v (t) = 230 √2 sinωt where ω = 2π × 50 rad/sec. The input current drawn by the rectifier is given by

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

The input power factor, (rounded off to two decimal places), is, ________ lag.

To find the input power factor of the AC-DC rectifier, we analyze the given voltage and current waveforms.

The input voltage is:
$v\left(t\right)=230\sqrt{2}sin\left(\omega t\right)$

The RMS value of the input voltage is:
$V_{\text{rms}}=\frac{230\sqrt{2}}{\sqrt{2}}=230\text{ V}$

The input current containing fundamental and harmonic components is:
$i\left(t\right)=10sin\left(\omega t-\frac{\pi }{3}\right)+4sin\left(3\omega t-\frac{\pi }{6}\right)+3sin\left(5\omega t-\frac{\pi }{3}\right)$

The total RMS value of the input current is:
$I_{\text{rms}}=\sqrt{{\left(\frac{10}{\sqrt{2}}\right)}^2+{\left(\frac{4}{\sqrt{2}}\right)}^2+{\left(\frac{3}{\sqrt{2}}\right)}^2}=\sqrt{\frac{100+16+9}{2}}=\sqrt{\frac{125}{2}}=\sqrt{62.5}\approx 7.9057\text{ A}$

The RMS value of the fundamental component of current ($I_{\text{1,rms}}$) is:
$I_{\text{1,rms}}=\frac{10}{\sqrt{2}}\approx 7.071\text{ A}$

The distortion factor ($g$) is calculated as:
$g=\frac{I_{\text{1,rms}}}{I_{\text{rms}}}=\frac{10/\sqrt{2}}{7.9057}\approx 0.8944$

The fundamental displacement factor (FDF) is the cosine of the phase difference between the voltage and the fundamental current component:
$\text{FDF}=cos\left({\phi }_1\right)=cos\left(\frac{\pi }{3}\right)=0.5$

The input power factor (IPF) is the product of the distortion factor and the fundamental displacement factor:
$\text{IPF}=g\times \text{FDF}=0.8944\times 0.5\approx 0.4472$

Rounding off to two decimal places, the input power factor is 0.45 lag.