In a two element series network, the voltage and current

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In a two element series network, the voltage and current respectively given as,
v (t) = 50 sin (314t) + 50 sin (942t) V
i(t) = 10 sin (314t + 60°) + 8 sin (942t + 45°)
A, then the power factor of the network is approximately—

1. 0·9
2. 0·6
3. 0·3
4. 0·1

Correct Option: B

Given,
V_(t) = 50 sin (314t) + 50 sin (942t)V
i_(t) = 10 sin (314t + 60°) + 8 sin (942t + 45°)A
Average or Real power or True power = Power of fundamental + Power of harmonics
or

P_av =	50 × 10	cos 60° +	50 × 8	cos 45°
	2		2

= 125 + 100 2

Reactive Power =	50 × 10	cos 60° +	50 × 8	cos 45°
	2		2

= 125 3 + 100 2

Now, Power factor =	Average Power
	Apparent Power

Power factor =	125 + 100 2
	(125 + 100 2)² + (125 3 + 100 2)²

or
Power factor ≈ 0·6.